V....
I know the sleep deprivation and it kills! Hang in there!
I don't know if your'e familiar with "The Baby Whisperer" books written by Tracy Hogg. I think her strategies could really help you in dealing with this difficult habit. Tracy says in her book that as far as how we set up routine with our kids, "Don't start anything you aren't willing/able to continue for the long haul." (paraphrase)
I know what it's like when a child works herself up into such a state that she would throw up...been there, done that.
You are the parent. I would suggest a plan of several nights (you and your hubby can trade off) committment to helping her make this transition (just like getting a child off of a pacifier). Explain that she needs to go to bed without the sippy cup and that you will help her. Try a different nighttime routine, i.e. instead of the sippy cup, you'll read or sing songs or make up a story together. Does she have a favorite blanket or stuffed animal she can sleep with? You may have to start by letting her have the sippy cup for a certain amount of time and then take it away, and gradually reduce the amount of time she has it until the night when you tell her "You're a big girl now, and big girls sleep without a sippy cup"...whatever you think she would respond to. It's important, though, to establish the fact that you are the parents and that a 2-yr old does not dictate how things are done in your home. Anytime you find yourself saying, "She WON'T LET ME......." you know that somewhere along the line you've abdicated your parental authority.
This too shall pass...and you'll get through it with flying colors. Hang in there and good luck!
T.