the coalition built for gulf war 1 was extensive to say the least. I think that was one of Bush Sr's requirements, if anyone was going to liberate Kuwait it had to be everyone. You would have to sanction the entire coalition which was basically the entire western world.

Bush Sr. convinced everyone to stop at Iraq's border and wouldn't push further to knock out Hussain's regime. Wisely, IMO for all the reasons that are clear today. However, lots of people think this is what cost him a second term and left many people at the pentagon feeling like there was unfinished business in Iraq. This "unfinished business" is what eventually led to Bush Jr's invasion.

Actually in the end the US went soft on Iraq. Thatcher wanted to roll into Baghdad and clean it out properly (or, she argued we’d find ourselves there again in a decade or 2). Bush disagreed.