Why are you (OP) not going through your insurance and letting them deal with all of the headaches, etc. associated with
payments, repairs, worry, etc. for this issue?
It is one of the reasons people carry automobile insurance. Let your insurance company go after the at fault party - or their insurance carrier.
Why burden yourself with all of this unnecessary overhead?
Typically, a person's auto policy takes care of paying for the collision repairs. If another party is legally "at fault" then the insurance company seeks
recovery damages from the other party and/or its insurance carrier. With this model, it may end up with lawyers from one insurance company negotiating
with lawyers from another insurance company.
If you run into issues receiving payment to cover your losses, how will that be handled? You'll likely have to obtain the services of a lawyer at your
expense, then try to recoup those costs in court. Who wins? The lawyers. Who loses?