It depends on your state to determine if your UIMPD will cover a rental car, but it likely will not pay for it.

It is not intended to cover rental car, the other party's Property Damage Liability should cover your rental car if what you state is accurate. Alternatively, your RREIM (Rental Car Reimbursement) should cover it if your insurance company is handling your claim.

Underinsured Motorist Property Damage covers when property damage is sustained by an insured and the negligent operator possesses insurance, but the limits of liability carried by the negligent driver are not sufficient to cover the damages. 

Underinsured Motorist Property Damage alone is not enough to cover all potential car repair/replacement costs, and only applies if you are involved in an accident caused by a driver without enough liability insurance coverage.