H.S.
Hi, J.,
I learned too late with my first that if you start them with water or juice in the sippy cup, it is very hard to get them to take milk from the sippy cup after. It is better to start them with milk and nothing else in the sippy cup until they've gotten the hang of it.
One way to trick them into taking milk from the sippy cup is to start by adding a little milk to the water everytime and slowly increasing the ratio of milk to water over a couple of weeks.
You might also try to forgo the sippy with milk for now and see if you can introduce milk in a cup with straw rather than sippy. As I recall, this was the method that worked for my first child (though it's amazing how quickly we forget these things). The straw took a little while to learn, but she got it eventually. And milk only until she was taking it without problem.
I remember this being a frustrating little hurdle, but you'll succeed!
Good luck!
H. S