Sue the drunk driver: he or she was by definition driving negligently, or carelessly, since it is negligent to drive drunk. Therefore, the drunk driver is him- or herself liable for your costs and losses. Even if he or she does not have applicable coverage, you can recover from him or her personally, including by possibly garnishing wages, putting a lien on real estate, or levying on any bank accounts.Also sue the rental car company, since they will not voluntarily settle the case. As a general matter, the owner of a car is liable for the damage down by at-fault drivers whom they allowed to drive their car(s). That said, it is possible that the rental car company may have a good defense, since DUI is also a crime, and an innocent party is often not liable for the criminal acts of others, even those who borrow or use its vehicles, since driving DUI or committing a criminal act using the car is clearly not part of the rental agreement; but if you name them in the lawsuit as well as the drunk driver (you sue both of them), that may motivate them or their insurer to offer you something to settle the case and avoid the cost and uncertainty of a lawsuit.