George Sr. was quite explicit in his book that he thought occupying Iraq was a Bad Idea. He even used the phrase “no exit strategy.”
This is not a war inspired by Daddy but by Mommy. People who know the Bushes know that Barbara is a really nasty person and that Dubya is her son. So Dubya has a really strong “get those suckers back” attitude that, while appearing supportive of his father, actually is against his father’s mores.
I don’t think Gore would have attacked Iraq. There would have been no good reason to do so. Of course, there was no good reason for Dubya to do so and he did it anyway, so my logical approach to this is perhaps misplaced.