Just a quick suggestion, if they don't cook already, you might encourage them to cook themselves. This is the way I have gotten a super-picky meat and potatoes man who never ate a vegetable in his life (except corn, which doesn't count) to eat asparagus, onions, peppers, squash, even tofurkey and Yves bologna! His tastes are changing and it's because he has found that he enjoys cutting up food and cooking, he makes mostly soups, but, hey, I'll take what I can get and they're delicious!
Maybe you can get a few fun kid-oriented cookbooks and go through them together, picking out foods that your kids might want to try making. If they have input into what goes into something, it might not seem so foreign to them and they might just start liking what they cook!
