My 20 month old loves Silk Plain Soymilk. Have you tried soy yogurt with her? There are also some really great yogurt drinks out there. My daughter just tried the Trader Joe's Strawberry Soy Yogurt drink, and she ended up drinking the whole thing!!! Also, have you tried giving her sips from your cup/glass. In a toddlers world whatever mommy and daddy are drinking is somehow better then what is in their cup. (Even if it is the same thing!) You might want to try a small 3 oz dixie cup. It might make her feel independent that she can have a big person cup. Just make sure you sit with her.
About the breasting feeding at home thing. My daughter does the exact same thing!!! I am with her all day at her School, and as soon as we get to the car its "Leche" (we are teaching her spanish) I think it is a comfort thing. She had a hard day working, and now she needs some snuggle time with mom.
Sometimes if she has nursed quite a bit at night and wants more, I tell her that the milk is all gone, then a offer her Soymilk, and she is fine. So try the milk all gone trick, and offer her food or a cup. She might get mad the first couple of times, but it will all be better in the long run. Good luck to you!!!