Here's a new timeline from my alternate history message-board. The gist of it that the Persian Gulf War begins a few months later than it did in our history, Iraq invades Saudi Arabia as well as Kuwait, and Yemen joins the fun by attacking Saudi Arabia from the south and mining the entrance of the Red Sea (presumably to prevent naval interference via the Suez Canal).
Behold, Lines In The Sand: A History of the Gulf War.
I was around six years old during the Gulf War and my uncle was in the Marine Corps. He went to the Persian Gulf and was part of the decoy force that made Saddam think the liberation of Kuwait would come by a naval invasion rather than "Hail Mary" offensive that hit the Iraqis from the west through their own country. Given how my uncle was involved, I was greatly interested in what was going on and watched CNN a great deal. I was obviously very glad to see Saddam defeated and retained the rather negative image of the man in my head for many years, contributing to my early support for the 2003 Iraq War.
(Which was not a good idea for a variety of reasons that have nothing to do with Saddam and his sons being a bunch of wicked hooligans who deserved what they got. Once exposed to anti-war arguments that consisted of something other than war-for-oil conspiracy theories and race-related tangents, I came to oppose it.)
However, I vaguely remember something from that time period about people getting their hands chopped off. In retrospect, I'm thinking those were arguments the anti-war people were making about how oppressive the Saudi and Kuwaiti governments were. This article here references anti-war people mocking the idea that the Gulf War was a war for freedom/self-determination, while there was an article in the (very) left-wing magazine Counterpunch that claimed the Iraqi annexation of Kuwait was welcomed by oppressed foreign workers and others. The article I linked to isn't the one I remember, but it makes the similar point. The Kuwaiti government promised to let women vote once the Iraqis were ejected, something that took quite awhile to accomplish.
(To be fair, that seems to be the result of popular sexism being represented in the Parliament, not Kuwait's ruler being a particularly sexist fellow.)
And then there's our dear friends the Saudis, who persecute Christians (and to add insult to injury would have hanged an underground church leader on Christmas Day), support al Qaeda, spread the poisonous Wahabi ideology, persecute Shi'a Muslims, tyrannize women and foreign workers, execute people for witchcraft, etc. The ruling class imposes a harsh brand of Islam on the people while blatantly not following it themselves. They interfered with U.S. soldiers' religious practices (trying to ;find third-party corroboration of this is hard), even though there was a joke going around at the time that the Saudi anthem should be "Onward Christian Soldiers." The House of Saud deserved a post-9/11 liquidation far more than the Ba'athist regime in Iraq did, if we're using support for terrorism as the metric.
So sufficient to say, the idea of Saddam and some allies kicking the hell out of the House of Saud is greatly appealing. And the Saudis took the Asir region from Yemen back in the 1930s, so them joining the fun is perfectly understandable. And author Neo_Desperado said that if things go well, the Jordanian monarchy might throw in with Saddam in order to reclaim the Hejaz, which the Saudis took away from Hashemite dynasty. In the timeline, the U.S. is rushing to reinforce the Saudis, but the author has compared it to the early days of the Korean War, in which our boys didn't do so well at all.
The idea of the U.S. losing a war doesn't appeal to me (or taking over-many casualties in a victory, which in this timeline could easily include my uncle), but the dismemberment of Saudi Arabia (I suggested a restored Hashemite state in the Hejaz, an independent Shi'a state in the Eastern Province, the Yemenis taking back the Asir, and the al-Sauds reduced to a rump in the Nejd where the al-Rashids can destroy them later) would be quite interesting. Perhaps after the Iraqis get the thrashing the timeline's opening photo implies they (eventually) get, some kind of arrangement that liberates the peoples of the Arabia Peninsula (natives and foreign workers both) from their backward feudal rulers and from the looting-happy Ba'athists would be in order.
If I didn't have so much else to do, I'd gladly help write an alternate-history story or even a novel set in this timeline. It could be told from the perspective of the Jordanians marching south into the Hejaz, to provide relatively sympathetic protagonists. The Iraqis could be, in TVTropes terms, the "Token Evil Teammate" and when the time comes for the U.S. to go all Norman Schwarzkopf on them, they can get the worst of it.