Here goes. After this be lots of spoilers, so be ye warned...
*The first twenty to third minutes of the movie--until the arrival of the alien mothership--are generally fine. However, I'd build up Jake Morrison (Liam Hemsworth), Dylan Dubrow-Hiller (Jessie Usher), and Patricia Whitmore (Maika Monroe) more. Dylan could be struggling to live up to his heroic stepfather's image, the orphaned Jake could resent Dylan for having a father figure, let alone a famous one, and Patricia could obviously chafe at abandoning her pilot dreams to care for her ailing father, the former President Thomas Whitmore (Bill Pullman). Crucible touches on a lot of this, but the movie hints at it at most.
Also, even though this risks being a "young adult dystopia cliche," some kind of love triangle would be interesting. Each man would have traits Patricia finds interesting (or unattractive) and just how and why she's drawn to particular personality would develop her character more. Crucible established that she and Dylan were close friends for years after the events of the first movie. Patricia might find comfort in the familiar as her father deteriorates, but also (as the novel points out), she view him as more a brother than a potential partner. Meanwhile, the wrong-side-of-the-tracks Jake might have a bit of a bad-boy thing going, plus she could be attracted to the scruffy look as opposed to the smoother Hiller.
(Also, interracial sparks between the African-American Hiller and the Caucasian Patricia not raising eyebrows would show how the post-invasion society has evolved beyond intra-human racism.)
On the matter of Jake being a "bad boy," the stuff he mentions having done (i.e. stealing a spaceship to visit Patricia) would get him kicked out of the military, or at least demoted to somewhere he couldn't cause significant damage (i.e. not flying a huge spaceship, even an unarmed and slow one). I'd nix the spaceship-stealing completely and depict him as simply having been kicked out of the fighter-pilot program due to nearly killing Hiller by mistake during an exercise and reduced to piloting a space tug just like Crucible depicts. To make it clearer, he's regularly warned by his hard-ass commanding officer that one more screw-up and he's gone completely.
I'd also nix the "Dr. Okun awakens after 20 years in a coma" subplot and just depict him working in a lab with a tentacle-scar across his neck and perhaps more eccentric than usual.
*I've never seen any of the actors outside of this movie so I don't know if their underwhelming performance was the result of a poor script or their own lack of ability. The actors who played Dylan and Patricia in the original film could have been brought back, if they were interested and could handle more demanding adult roles.
*When the alien mothership arrives, I'd depict the battle in space as much less one-sided. The humans should have been spinning up the plasma-cannon satellites from the moment the mothership appeared (or at the very least when it engaged the lunar bastion), so the Asia-Pacific defense grid shouldn't have been wiped out before a single one could fire. The human victory in the first film only occurs because the City Destroyer attacking Area 51 took so long to fire its main gun Russell Casse could kamikaze it. The human military planners would know that these weapons need time to "charge" and plan accordingly.
*Once the mothership blasts through the nearest orbital defenses and lands on the surface, I would depict all the other satellites reorienting on the mothership and firing, huge numbers of nuclear and conventional cruise missiles fired from naval ships, etc. Submarines in particular would be good attackers since they're harder to spot and hit than surface ships. The mothership can then launch fighters to defend itself, fire its own weapons at attackers, etc.
(Smarter aliens would stay in orbit and either bombard ground targets directly or deploy smaller ships to attack, but having it land allows for the "space-tug death ride" sequence to stay. However, this one would have flying missiles, conventional and nuclear explosions, alien fighters, etc. replacing the landmarks from Singapore pulled into the air and dropped on London. Seriously, the mothership isn't big enough to affect gravity like that.)
*Hiller is ordered to retreat to Area 51 when the aliens triumph in orbit, but he detours to what looks like New York City to see to the welfare of his mother. That's playing fast and loose with both his own life and a very valuable piece of equipment, something that should get him into trouble. I would have him follow orders to return to Area 51, then call his mother, and have her die while on the phone with him. Maybe she makes it to the helicopter but it gets shot down by alien fighters clearing the airspace around their ship?
*Julius Levinson (Judd Hirsch) should have died. This would hurt David Levinson (Jeff Goldblum), especially if their last conversation had been hostile. Furthermore, given how the elder Levinson begins the movie by claiming credit for saving the human race (because he suggested they give the aliens "a cold") and Whitmore's nightmare implies the Harvesters have been listening to human radio and television transmissions, the aliens might take a personal interest in hunting him down. If we don't see him die in his boat when the alien uber-ship lands on the Atlantic coast, perhaps some aliens hunt him through the ruins of Florida and corner him, then hold up a waterlogged copy of his book before blowing him away? It could be a bit of dark comedy.
(If the mothership remained in orbit, a wave of Excalibur missiles could clear the way for nukes or more powerful weapons--see below for ideas. A laser-missile could strike from farther out, avoiding fighters, defensive lasers, etc. that could shoot down a nuclear-tipped missile.)
*Give the hybrid fighters missiles so they can hit the alien fighters from beyond visual range. Crucible references the fighters carrying missiles as well as the energy cannon, so depicting them firing off a wave of missiles before they close to knife-fighting range like the first movie would make more sense. Crucible describes missiles able to exploit the alien shields' "phasing" to slip through, so they could do more than bounce off the big ships' force fields or knock fighters around like the Sidewinders did in 1996. Failing that, Excalibur-type missiles that could punch through shields like a knife going through a force-dispersing Kevlar vest.
*Ix-nay on the "cold fusion bombs." As far as I know, cold fusion isn't anything different in terms of energy production from conventional fusion. I'd have made the post-nuclear superweapon antimatter. If the Harvester ships run on antimatter, it would explain why Casse's suicide run was so effective--it ruptured the antimatter fueling the City Destroyer's main weapon and the resulting explosion ruptured the antimatter fueling the engines and other important ship systems. We're capable of making small amounts of antimatter now--imagine how much better we'd be with captured antimatter-production technology.
*The bit about the aliens drilling for the Earth's core is absurd. If it's minerals they're after, the Harvesters could get them from dead worlds, asteroids, etc. much more easily. President Whitmore's mind-meld with the aliens in the first movie made it sound like they intended to colonize the Earth, use it up, and move on. If the mothership lands and immediately disgorges armies of soldiers and colonists, the aliens' strategy could be that the humans wouldn't immediately nuke the hell out of the landing zones for fear of hitting civilians intermixed with the aliens.
*I didn't mind the friendly alien coming to rescue humans from the Harvester colonization fleet. But instead of offering to take humans to a hidden planet to join the interstellar resistance against the Harvesters, perhaps it supplies schematics of the mothership and advice on how to destroy it? Given how the mothership is 3,000 miles wide, I imagine it would require a hell of a power source and destroying that could be the key to victory. That could have been its purpose in the first place--the alien could have known the humans were advanced enough to, with some help, defeat the even larger Harvester fleet. If given the choice to definitely save a few people (the possible reason the Rhea base went offline) or possibly save a whole species, I'd go with the second choice.
*I would have made the destruction of Cheyenne Mountain and the death of the current president a lot more impressive than some alien commandos blowing down a door and shooting everybody. The command center is way down inside the mountain--the aliens would need to drill down to get to them. Remember, the mountain is designed to survive nuclear hits. Either have a more impressive alien ground attack, have them blast through it with their giant energy weapon like they apparently did in the first movie, or crack the mountain open and then send in the commandos for an epic two-fer of slaughter.
Furthermore, the entire line of succession wouldn't be present to be conveniently killed off. Think how the designated survivor is always away from Washington DC in case a terrorist takes out everybody. I'd have made it so General Adams is in de facto command because owing to the loss of satellites they can't find any Cabinet-level officials, the Speaker of the House, etc. after the president is killed in Cheyenne Mountain, but he wouldn't be formally sworn in as president. As far as I know, the chairman of the joint chiefs is not part of the line of succession. When the movie ends they find the designated survivor and Adams cedes power back to him, thus reaffirming civilian control and constitutional governance.
(One-third Americans think a military dictatorship is preferable to the current crop of civilian politicians, so this would push back against that abominable notion.)
*The climactic battle is a renewed assault on the mothership with the goal of getting through to its core (with the help of human pilots whose planes had been shot down in the initial assault who are doing a Die Hard inside the ship like in the film) and blowing it up. Triggering an antimatter explosion to "hollow out" the ship within its shell would hopefully do less damage to the world than a nuclear or antimatter strike intended to blast through the aliens' armor (or shields if they're back up) and smash the ship to bits from the outside. To build suspense, alien fighters and ground forces are spilling out of the mothership, so if it isn't destroyed by conventional means before a certain point, the humans will nuke it, killing millions of nearby civilians and possibly causing enough destruction that, along with the damage it did when it landed, the Earth's climate would be wrecked. That's a better "doomsday clock" scenario than the "the aliens will get to the Earth's core in an hour" business.
Plus, between the burning cities and the possibility of large-scale debris from the mothership raining down, it's possible that many if not most of the three billion deaths from the first invasion were the result of famine (and consequent disease) from an impact winter like the one that killed the dinosaurs. This is something the survivors would desperately want to avoid--hence the risky plan of trying a second "get inside and blow it up there" the aliens will likely expect rather than just unleashing every ballistic missile and bomber on Earth on the thing.
*Instead of the aliens being a Keystone Army where the death of the queen causes all of the fighters to crash, make the Harvester Queen a sort of big-boss creature instead. All the other aliens dying after the fall of the Harvester Queen at Area 51 contradicts the first movie in which we see a human fighter pursuing an alien fighter after the mothership is destroyed. Independence Day Crucible also features Captain Hiller helping Russians fight a bunch of alien survivors barricaded in an old Soviet military base and a decade-long battle between African warlords and the aliens from one surviving City Destroyer. If there was a queen whose death would cause the death of all the other aliens, she would have died on the mothership and there wouldn't have been any fighting afterward. We could give Whitmore his death ride against the Harvester Queen like in the film--he rams her with a space-tug carrying troops for the commando mission, her personal shields protect her from immediate death, so he turns on the fusion drive and slams her into an interior wall (or into the antimatter core itself for good measure), wiping out both of them.
With the death of the queen and the destruction of the mothership, the aliens on the surface have to retreat from Earth using smaller ships (like the vehicle the queen took to Area 51 in the actual movie). Alternatively, there's something similar to the montage of fallen City Destroyers from the first movie where the remaining alien forces are destroyed on the ground. That would much more sense than "with the queen dead the fighters fall from the sky and the other ships retreat to serve a new queen" bit the friendly alien supplied.
*The ending, in which the humans are recruited to fight for the friendly alien and some others who'd been at war with the harvesters for thousands of years, should be a bit less hopeful. The eccentric Okun can claim that with interstellar travel humans could "kick some alien ass," but if the war's been going on for thousands of years, humans are the equivalent of the Indian war chief Red Cloud and the Harvesters are the United States. We bloodied their noses a couple times and avoided colonization/extermination thus far (just like how Red Cloud won his war against the United States), but we're at a ludicrous disadvantage. Somebody should mention that, or at least act so grimly that Okun's enthusiasm obviously dims.
*All this is a very tall order for a single film and would no doubt be incredibly, incredibly expensive. However, if the story were broken up into two films, this would be more doable. The first film could climax with the epic battle in orbit, the death of Dylan's mother and Dr. Levinson's father, and the alien landing and end with Dylan, Jake, etc. rallying the survivors under General Adams for a counterattack. The second film could begin with the counterattack, have the dark spot in the middle where it fails (with most of the pilots killed or trapped in the mothership) and the aliens strike back by wiping out the president and most of the cabinet, and then have the second assault on the mothership be the climax. A gamble, but the last Hunger Games and Harry Potter movie adaptations were split in two, after all. It would also allow for more room for character interaction and development.
Independence Day: Resurgence could have been a three-hour special effects extravaganza or even broken up into multiple films. Instead we got something mediocre.