For starters, Hart shouldn't even meet Donna Rice. Alternatively, if you think he's too much of a horndog to not be caught womanizing, Hart's wife dies in a car accident in 1985 or something, making his behavior semi-acceptable (and also giving him less time to womanize, since he's busy raising his kids).
Clinton contemplated running in '88; had he run, Gore probably doesn't run, since Clinton fills the same space that Gore did. At the same time, Clinton himself probably doesn't win.
Not sure if Hart would be able to win the '88 primary. He was the frontrunner... in 1987. Still, it shouldn't be impossible, nor should it be impossible to win in the general election.
I think a Hart-Gore ticket might be possible, though Hart-Clinton might be better - Clinton's charismatic enough to play the attack-dog role effectively.