As I recall, Bush Sr was very emphatic about not wanting to remove Saddam as that would lead to an occupation of the country, which he didn't want to risk. I think the only way you can get this is if Saddam is KIA by US/Coalition forces. I don't know enough about the specific events to speculate on the plausibility of that happening, but if it does, you likely won't see a lot of the mistakes made after Saddam's OTL fall (like de-Baathification and the dissolution of the military).