Hi E.,
I would suggest you look at this from a different angle. Why does she not want to eat? Eating is not a discipline, it is a joy when our bodies want and crave it. Her body neither wants nor craves it.
What if your daughter is experiencing digestive pain and she knows eating is going to make it worse. Her brain knows, her body knows, she just doesn't yet know how to explain it. Food sensitivities and allergies as well as fungal and bacterial overgrowths are huge problems with children. If she does not have regular (1-2X per day) bowel movements that are firm (not loose or hard), you can be sure she is struggling.
You can do a number of things to see if you can get improvement before you spend money on medical testing.
1) remove all cows milk products from her diet (milk, yogurt, ice cream, cheese). Substitute rice milk for her milk.
2) Add 1/2 tsp cod liver oil, 1-2 capsules of proibotics (emptied into juice), and even get some chewable enzymes (like Zyme Prime)
3) Remove all processed and non whole grains from her diet (yes, that means cheerios and gold fish).
Get to the basics with fresh meat, veggies, rice, fruit, etc.
Your daughter is trying to tell you something. Don't miss it assuming she is asserting herself or being willful. Find out why she is asserting herself - what is she crying for, listen closely. At worst, you will find that she feels better, is less grumpy, and more willing to work with you. If you want more info on how to do the testing, just send me a note. Thanks, J.