I agree with your daughter...rice milk is definitely not the tastiest! I tried to mix it with other juice to make my son's formula, but he wont' drink it. I can only use it in baking.
If you want her to drink it, you might try almond milk (just make sure she's not allergic to nuts first). I think it's tastier, and higher in fat. We are moving to almond milk for those reasons ourselves. You may still need to add chocolate/strawberry syrup to it for flavour. I think your daughter is about the same age as my son. Is she still on formula?
If you are making pudding, try coconut milk. Or, I'm just about to post the websites with dairy free recipes. There is one in there for chocolate tapioca pudding. It is so delicous. Your daughter might not like the texture of the tapioca, so you might need to make just chocolate pudding. But trust me, she will love the chocolate pudding made with coconut milk. It's so creamy....I think I might need to make some tonight for dessert

I'm obviously no expert on food challenges, but as a mom with a baby with severe food allergies, I would be very hesitant to just change her foods and start giving her diary. Her system is not used to it, so it might upset it. I would probably check with your doctor, or give just a little bit and see how she does. Let me know how it goes.
I'll make a new post about the websites/blogs.