Glad you are all OK. You should all be checked out by a doctor. You will no doubt be more sore and stiff over the next few days.

Use your insurance company. You have agreed value coverage for a reason. Principle is no reason to insist upon using the other driver's insurance company, especially with this car.

As far as keeping the car, your insurer will deduct the projected value of the salvage from the settlement amount should you decide to keep it. This is another reason to use your own insurance.