Personally, I wouldn't do it. Of course, I also hate my ex, so I might not be the best to advise on this.
I tend to be of the opinion that you got divorced for a reason...whatever that reason was. Those reasons generally don't go away. Some could, sure: she could lose weight, you could quit drinking. Reasons like that, if proven to have been resolved, would not preclude getting back together, if those are the sole reasons the marriage ended.
It's the other reasons, the real reasons that most people get divorced, that don't go away: the one is bad with money, cheating, lying, finding fundamental differences in your feelings on parenting/marriage/life.
Even though someone can claim to have changed in those areas, I don't think that's true very often. Things like that are often from the way a person was raised, and even if they don't 100% agree with it, most people tend to fall back on it simply because it's familiar. It's what they know, and change scares most people.
I doubt very much that going on a date with her would do much of anything except to get your kids hopes up, and leave you two frustrated all over again.