As JD said, you would know much better than we would, what your kids would like, but BSV seems like a perfect base camp for all of you to get together when you want and have the 'kids' take off on their own when they want. Certainly folks can walk to Maho during the day if they like, but not at night, also walk to Karakter during the day, but again, not at night.

As far as Flamingo, to my knowledge, they do not have a/i at Flamingo. Flamingo is a more convenient place for them to be able to walk to a bunch of different places, including the casino, Red Piano, etc., though. Not sure whether you're traveling during season or off season. As far as COST is concerned, if you travel off season and stay at BSV and cook in or get carry out for several meals, it would be a fairly economical trip.