If my daughter hit a deer in a friend's car but she is not covered under her friend's insurance and the car is in the mother's name, what should we do?
Since your daughter's insurance does not cover her for liability and damages if she drives another person's vehicle, you need to change your daughter's coverage to include such coverage in the future.
As to the current problem, most likely the car that was damaged by the struck deer is insured under the friend's mother's policy. I suggest that you check to see if that is the case. If so, then the mother's isurance policy should cover the damages needing repairs. I would at least offer to pay the deductible required for the repair of the car since your daughter was driving the vehicle when the incident happened.
Actually, your daughter should pay the deductible for the repairs since she was the driver at the time of the mishap regardless of the fact that she probably could not have avoided the striking of the deer.