Is it permissible to accept compensation for an injury sustained in a car accident to repair a damaged car belonging to one's sister, knowing that the car's insurance does not cover the damage and the sister is not wronged, while the injury insurance does cover it?

Commercial insurance of all types is forbidden because it involves gharar (excessive uncertainty), maysir (gambling), and riba (usury). The insured is only entitled to the premiums they paid, and they have no right to anything beyond that. It is not accepted that insurance is a necessity, nor does its permissibility in a certain country make it lawful, for what is lawful is that which Allah has made lawful, and what is forbidden is that which He has forbidden.