IMHO, it sounds like a bigger problem than you can deal with on your own. I am sorry you are going through this.

I second Lisa in suggesting that you immediately get a complete physical for your daughter and if there is no physical reason for the hunger, consult a professional counselor. If you can't afford a private one, and don't have insurance that will pay for it, many religious groups offer counseling on a sliding scale and you don't have to be a member of the religion to take advantage of it. Catholic Charities are all over the place and Lutherans, Jews, Quakers, etc. have counseling services as well in many places across the country.

If it were my daughter, I wouldn't try to start her on low carbing without first having a complete physical and consulting with some professionals, unless she is asking to lowcarb. IMHO, getting into a battle with your daughter about food is not a good idea, and forcing her into low carbing when it is not her idea may well turn into a battle. My parents tried to control my eating when I was that age and what I learned was how to sneak around and get food behind their backs. I'm still dealing with the ramifications of that.

Also, and please don't take this the wrong way, look at the title you gave this thread, "This is the last straw." To me, that title seems to imply that you see yourself as fighting against your daughter, rather than working with her. I think you need to find some way to work with your daughter to solve this problem, instead of trying to impose a solution on her. I say that from hard experience -- I fought my oldest child for a long time (not over food, but over other issues) and it took a lot of counseling for me to learn to work with him as a team instead of trying to fight him and mold him to be the way I wanted him to be rather than letting him be himself, faults and all. If you are feeling that way about your daughter, she probably senses it, and that could lead her to be even more stubborn about the eating.