Have you tried the cups with straws instead of the regular spouts? Mine wouldn't take a sippy cup either, but one day at a restaurant he saw me drinking my water with a straw and wanted to do that, so I gave him drinks from my straw by holding my finger over it and letting him suck the water ut. He loved it so I went out and got him the straw kind. They say they are for older kids, but there is no reason littler babies can't use them as long as they can figure them out. I use the Munchkin ones, you can get them at Target and sometimes Walmart. All the parts can go in the dishwasher if you have one of those baskets, and there are no yucky valves to deal with.
Maybe since she is doing water in the sippy, it has something to do with how thick the liquid is. Sippies are hard work for them, and formula is a lot thicker than water. There are Take N Toss cups that are pretty cheap, and they have no valves. So the liquid is easier to get out. But they will leak. But maybe that would be an easier transition cup, at least until she is on whole milk and not formula,then you can go to the other kind.
Good luck!