Make a meal and offer it to them. If she is really hungry, she will eat it. All she is trying to do is take control of your relationship. I guarantee if she doesn't eat lunch and dinner the first day, she will eat anything you give her the second. By the way, if you are thinking that is harsh, its not because you are offering her your food whenever she wants it.
If you let her dominate you, she will turn into a spoiled, picky eating brat that wont eat anything except peanut butter and eggo waffles (not that i have anything against either).... And no body likes a picky eater, especially if they are a brat =).
**note, this is the time to get your kids hooked healthy foods that TASTE GOOD, so try satueed veggies and baked chicken with seasoning, etc, not fast food or junk food