My son used his bottle FOR MILK ONLY until he was 2.5. I had no problem getting him to drink other liquids out of a sippy cup during the day, but he would not drink his morning, nap time, and night-time milk unless it was from a bottle. I was of the opinion that getting him to drink his milk was far more important than what he used to drink it with. And, there are many children still nursing at that age. I don't think there is any difference. Both are to give nutrients and for comfort. (Remember, doctors are for giving MEDICAL advice, but I do not believe that ANY doctor should be giving parenting advice. It is not their place!! We didn't tell the doctor about our bottle use. It was not his business and he didn't need to know!)
At 2.5 we made the decision to take his bottle away. It was very hard for about the first week! Regardless of when you take it away, its gonna be hard for the first few days to a week. However, when my son was 2.5, I could explain to him why we were taking it away, etc.
The one thing I would agree on is not to let him fall asleep with his bottle. My husband and I would rock my son or cuddle with him on the couch while he finished his milk. Once finished we would brush his teeth and either finish rocking him to sleep or put him in his crib if he was drowsy enough to fall asleep on his own.
As far as sippy cups that don't leak, I love the $1 nubby cups at Walmart. They are the simple looking ones with the white valves. Cheep and we don't seem to have an issue with them leaking. Good luck!!