D.S.
Hello S., This is something that has worked well for not only my own 5 children and 12 grandchildren but the Day Care children I have had. Get a sippy cup that has their name on it. Then introduce it as a big deal and literally destroy the bottle so you don't cave in to giving it back.
If you can't find one with the child's name then get one with a built in straw attached they come in many colors and sizes I personally have 6 different colors here that we use. I even take a marking pen and put the namealong the bottom so they know which cup belongs to them it makes them proud to know they have something noone else in the family uses. I have also found that I have had to tell some little ones that want a pacifer that it is time to pass it along to a younger child or baby if that helps any. I learned a long time ago to give all my children raw vegetables with a simple dip and they have been eatting vegetables w/o problems, they also drink v8 juice which helps as well.
Good Luck,