My guy is almost 2.5, and when he was turning 2 his pediatrician said to switch him to the 2% and just 2 cups of milk a day, otherwise he might not eat food as he should. She also told me that too much milk can cause an iron deficiency, something I had never known. BTW, I give him the milk in a sippy and measured it out, he actually gets 9 oz, so he gets 2 oz more a day than she said, I'm not inflexible, lol.
He had a cold about 2 weeks ago, and went through a rough 3 or 4 days where he couldn't or wouldn't eat, just wanted milk or juice. Naturally I didn't want him to dehydrate so I did let him have 3 cups of milk each day and juice 2 or 3 times. Lo and behold when he felt better he kept trying to demand milk and juice, for over a week. I just had to keep telling him, "You get milk in the morning and at night, juice once a day," (because of the sugar content.) He finally got over the "extras" a couple of days ago, and is eating much better again.
Like our ped said, if he eats yogurt or cheese he should actually drink less milk that day, so you can cut your daughter's intake to 2 cups a day or less if she eats dairy foods, and her appetite and willingness to eat food should increase. Milk isn't bad, there's just other things that are good for her, too, and you want to develop those good eating habits while you can. Like our ped said, I'm in charge of what he eats, he can't get it himself : )
Here's some ideas on getting her to eat, one of them is to not negotiate, meaning don't tell her she has to eat to get her milk:
http://kidshealth.org/parent/nutrition_center/healthy_eat...
Hang in there, she'll get better at eating!