How do I get my daughter off of bottle?

I'm trying to wean my 16 month old off of the bottle. I have tried pretty much every type of sippy cup there is. From ones with nipples to ones with straws and ones with spouts. There are two problems. She has no idea how to tip a sippy cup or her bottle for that matter. The other problem is that I have finally found a sippy cup that she can use because she doesn't have to tip it at all because it's the kind with a straw that goes all the way to the bottom of the sippy cup. She was using it fine with just water in it yesterday. This morning I have replaced one of her bottles and put the milk in the sippy cup. She drank the milk fine, but she refuses to drink water out of it now. I have no Idea what to do because she won't let me feed her water from the bottle and she won't use this sippy cup now, this is the ONLY sippy cup she is able to use. This problem has been going on for weeks no with me trying to get her to use a sippy cup that she has become dehydrated and it's caused her to become constipated. I have had to take her to the doctor to get a laxative for her because she went 9 days without going poop. This is now again the 7th day without her going poop. I have been giving her the laxative everyday, but because of her not getting any fluids except for milk, the medication isn't working. I'm at a loss for what to do. Any help?