Hi N.,
Does she drink juice and water from the cup, or does she just hate the cup? We had to experiment with several different sippy cups before my son would accept it. Then, we just took bottles away from him entirely so all he was offered was a cup. We didn't do this until he was about 16 months because he had a baby brother brought into the house at 13 months, and we thought this in combination with taking away his bottle would be too much. Still, we were somewhat concerned that he would see his brother with a bottle and refuse the cup, but he didn't. Sometimes they're just not ready when we are...
As for refusing milk, this is pretty common. My son drank tons of milk, but started refusing it a couple of weeks ago. I read quite a bit about it, and it seems that they only need 2 or 3 8-oz cups of milk (or the equivalent) per day. In fact, more than this can be detrimental to their health because it can affect the uptake of iron. Between age 1 and 2 is a crucial time for iron deficiency, which is a common cause of childhood developmental problems and can also negatively affect brain function and a host of other things.
That said, my son LOVES yobaby yogurt, which you can now get with fruit and cereal added. This type has DHA and 45% of daily iron requirements. My son will also eat cheese cubes, cottage cheese (especially mixed with fruit or applesauce), and milk with his morning oatmeal. So, I would suggest that you try some of these milk alternatives (although keep offering milk in the cup!!), toss out the bottle entirely when you find a sippy cup she really likes, and think about waiting a little longer if she's telling you she's not quite ready. She'll be fine! Happy Mother's Day!