J.L.
Hi K., since she's 10 months I would put her on a cup, I have an 8 month old in my daycare who is on a full time cup. If she has teeth the cup would be best for her, to help her teeth stay healthy, if breast milk is an issue, you can put in a cup, she mentioned she refuses the bottle, in my opinion that's a good thing, it kind of sounds like you give her a lot of control as to what she will drink in what, even At 10 months you need to be in charge, of what she eats and drinks and how, they learn how to get things their way at such a young age, instinct will not let her go thirsty or hungry if you don't give in she will eventualy change her habits. My kids did, I bent a little, but not enough to where they were in charge.
J.