Don't try to "win her over" by being foolish with your assets. She's already playing dirty pool.
Regarding the flying lessons: don't stop them because you want to stop her from seeing Shrek. That's the tail wagging the dog. Personally I think Karate 2X a week is a better use of time and more likely to become a routine GAL activity than flying. Just my vote.
I think it's fair to ask her not to expose the kids to him until after the D. You are not stupid, neither are your kids. It's fair for you to say that they mentioned they saw him. Duh. "Mommy was hanging around a big rotund man who sweat alot and looked like a troll."