If your mother was replacing a different car already on her auto insurance policy then this "new" used car may have been covered under the policy for the car that was traded in or otherwise being replaced.

A car dealer or the dealership typically has no responsibility regarding a consumer placing auto insurance on a vehicle. Once the consumer takes possession of the vehicle they are the one that should have at least the state required insurance on it so that it is legal to drive and park on public roadways.

The California Department of Insurance states that if you anticipate acquiring a new, replacement, or additional vehicle, contact your agent/broker or company prior to taking possession. It is necessary to determine what coverage will be extended and what coverage will have to be added to your existing policy. If the new vehicle is financed, also check with the lender for their insurance requirements.

The California DOI also states that most insurance policies within CA provide 30 days automatic coverage for a vehicle that replaces a vehicle already on your policy. The coverage normally is the same coverage you had on your previous vehicle. Notify your broker-agent as soon as possible of any replacement vehicle. If you wish additional coverage, there is usually a requirement that you notify your agent or your company within a designated time period.

If your mother was not replacing a car but adding a car to the policy or buying her first car to place on an insurance policy then she likely had no car insurance coverage at all since she had only received quotes and had not bought insurance for the car.

This all being said, since it appears your mother was able to identify who struck her car, and hopefully stopped the individual as well as called the police to make a report, then she should be able to place a claim for her car's damages with the at-fault party's insurance.

If the person's insurance doesn't cover them in the U-haul they were driving and they do not offer to pay for the damages personally then your mother may need to see about taking them to court and seek a judgment for the cost of the repairs to the "new" used vehicle.