1. You have proof that his car caused the damage to your car, therefore you.
2. He needs to show with evidence that he is not responsible for that damage. Based on what you said, he would have trouble show that.
3. If he has trouble to prove he is not responsible, then
he will tell his insurance company to defend (or cover for him).
4. At that point, his insurance company either defends him in court, or try to make you happy to make the case go away.
5. Now it is time to talk about damage to you. Cost of
rental is part of damage because of loss of use for you.
You have to do things in the right order.
You can't put cart in front of horse.