The simple solution is to simply not have the things she/he wants that you don't approve of in the house and only have healthy foods available. This is a bum deal for you if you want snacks, but it's a bit unfair to expect your kid to eat healthy if you don't anyway. That's the way I've done it. Kids will eat when they get hungry. My daughter is picky and this is the stuff she'll eat:
Cereal - we do a lot of organic and you can find really low sugar cereal, oatmeal is good too.
Eggs - I top them with a little cheese.
Soup, string cheese, a variety of fruits, applesauce, yogurt (especially lemon flavored), carrot sticks, celery (because the Wonder Pets love celery), raisins, ravioli (again, organic brands have less salt and sugar or make your own), mac and cheese isn't too bad if you make your own.
Snacks are things like a piece of bread, veggies, fruit, or some crackers and cheese. There is nothing terribly wrong with this so long as they aren't eating a bunch of junk and eating a variety. I let her have some cookies, muffins, and sweet breads too because we bake them and I make no sugar or low sugar recipes. It's not a problem for a kid to eat 4 cookies if they only have flour, eggs, raisins, dates, and coconut in them. She loves stuff like that because she helped make it and it looks like a cookie and it's sweet enough when she isn't comparing it to a toll house chocolate chip cookie. Good luck
