First, your insurance company will not cover any claims arising from accidents from drivers who drive your vehicles without your permission. So, your insurance company will not cover a claim resulting from your sister driving your mother's vehicle without your knowledge. Besides your sister, your elderly mother will be held accountable. The driver and the owner of the vehicle are held accountable for the driver's actions. Based on the information you have provided, you should not have any personal liability in this situation. You may want to pass this information on to your mother, though.