Since your daughter is taking her mother's car to California for summer and beyond for college she will need to be covered on her mother's policy. The mother should notify her insurance company of this situation.

Once the insurance company is aware of the situation, the agent should be able to tell your daughter and her mother where the coverage will need to be written. Typically, it will be in the state where her mother lives. It might help that both California and Pennsylvania have basic liability coverage limits of 15/30/5.PA also requires medical benefits of at least $5000.

If your daughter becomes the owner of the car, instead of just borrowing it from her mother, at that time she might need to register it in California and get her own California insurance policy on it.