Rental Car Exposures under PAP

Our named insured resides on outer island (Island of Kauai) and has one of his scheduled autos on another island ( Island of Oahu ) where his 23 year old daughter resides and is using the vehicle. The 23 year old daughter is not going to school on Oahu. The scheduled auto does have physical damage and liability coverage on it.

The insured's daughter gets into an accident with the scheduled auto and now is driving a rental vehicle while the repairs to the damaged scheduled auto are being done. The daughter rented the vehicle under her own name; the named insured did not rent the vehicle for her. Would there be liability coverage and physical damage coverage under the named insured's (parents) policy for the rental vehicle while the 23 year old daughter is driving the rental vehicle (should there be damage to the rental vehicle, or if daughter rear-ends someone)?