Michigan law requires you to have No-fault insurance (sometimes termed PLPD) as minimum auto insurance coverage. The basic Michigan no-fault auto insurance policy has 3 parts that include personal injury protection, property protection and residual liability insurance (bodily injury and property damage).
A person's property protection pays for damages to people's property, such as buildings and fences. It will also pay for damage your car does to another person's properly parked vehicle. It does not pay for any other damage to cars.
The residual liability insurance protects insured persons from being sued as a result of an auto accident except in certain special situations. You can only be sued for a few items, including for up to only $500 if you are 50% or more at fault in an accident which causes damages to another person's car which are not covered by insurance.
Under Michigan's No Fault law, you are responsible for insuring your own vehicle against collision damage. The mini-tort law lets you recover only up to $500 from the at-fault driver for damage to your vehicle. Basically the mini-tort $500 amount is usually enough to cover your deductible if you have collision coverage.
If you have an auto accident, Michigan no-fault insurance pays for your medical and wage loss and the damage you do to other people's property (not car unless parked). It does not matter who caused the accident. Your basic no-fault insurance does NOT pay for repairs to your car.
If your car is properly parked and hit by another car, the other driver's no-fault coverage will pay for the damage to your car. Except for this one situation, the only kinds of auto insurance that will pay for repairs to your car are collision and comprehensive coverage which you would need to carry on your vehicle.
This information above is from the Michigan Office of Financial and Insurance Services, the insurance regulator for the state. Here they make it clear that if you only have PLPD the most you will receive for damages to your vehicle from the at-fault party is $500 from the mini-tort law.
For damages above this $500 amount, your daughter would need to have collision coverage on her vehicle and would then make a claim with her own insurance company to get the repairs done. The at-fault party's full coverage (likely meaning collision and comprehensive) will allow that driver to make a claim with their own insurance provider for the damages their vehicle sustained in the accident.