K.J.
Maybe try to find a sippy cup that is entirely different than the cups she usually drinks water or juice from. We found some that were made by Nuby that were almost like a bottle that were a good transition.
Also, my son was on soy milk too and for some reason he really liked the fortified meijer organic soy milk. We tried Silk and other brands but that was his favorite. Its not in the dairy section its in the baking aisle so it took us a while to find it. The soy formula was really expensive so we were really excited when we got him drinking regular soy milk. He is 18 months now and has actually completely grown out of his dairy allergy so he's drinking regular milk now, which also took a while to get him used to.
My only other suggestion would be maybe just to stop with the soy milk completely and then try again in a week or two. That worked with my son when we were trying to get him to drink cow's milk. At first he would spit it out and wanted nothing to do with it or we had to mix just a little bit of it with the soy milk. So we quit trying and two weeks later my husband gave him a cup of it and he drank the whole thing. That trick has worked for us a bunch of times when my daughter was little too. I think you have to catch them when they're in the right frame of mind. :)
Good luck!