Hello,
In this case, it could be defined as a master-servant liability under the law of torts. Even though the driver is not the owner of the vehicle and she was the one who ran into another, as the owner you may be liable as you are the owner of the vehicle. You let her drive which means who acted as a master and she as a servant. During her course of employment, that is, as she was driving, she was performing as a servant to the command of the master. She ran into another causing accident, thus it is the liability of the master as she was working under the course of employment.
The law says that a servant during his/her course of employment commits an offence, it is the sole liability of the master.
Hope it is clear.