Did the other girl signal that she was going to stop or turn? If not, then the accident was her fault. Even in a car accident if the vehicle in front stops suddenly without signaling and causes an accident, they are often issued a ticket for being the cause of the accident.
As she was at fault, I would consider sending her (and parents) a bill for your daughter's ER visit and other accident-related medical costs. I can guarantee that what you are having to pay for the injuries is going to cost a whole lot more than the cost of a bicycle tire.
Of course, that's not legal advice.