3 cups a day is too much. I gave my toddler that, too, and she rarely ate much. Two cups a day is plenty...one with lunch, one with dinner. Also, actually measure out a "cup" and pour it into whatever she's drinking...you might actually be giving her 10 or 12 ounces a shot instead of 8.
Someone suggested changing from whole to 2%...at her age, she ought to be on skim milk. I'm not so thrilled with the idea of milk anymore period, and my youngest doesn't drink it, but my almost 8 year old still loves milk so I give her about 2 6 oz. servings of skim a day.
And, like everyone said, 2 year olds don't eat that much. Their appetites are super delicate, and an 8-12 oz. glass of milk with a meal, with her actually DRINKING the whole thing, could potentially spoil her appetite. Maybe try giving her 2 ounces in a little plastic cup and some food, and another cup with water? You can always refill the milk after she's taken a few bites, if she wants more.
My two year old eats better than most other toddlers...and she doesn't drink milk. She only drinks water. This wasn't MY choice, I tried pushing cow's milk on her for a long time...she just doesn't like it. But I do think that contributes to her having a better appetite. She'll eat a bowl of dried cereal or a waffle with peanut butter for breakfast, with a banana, a can of tuna or salmon with a cheese stick or yogurt and an apple for lunch, and maybe three bites of supper because by that point, she's full, tired, and ready to go to bed. That's just a sample of what she might eat in one day. Water all day long, at her request.