In my humble opinion:
The car should not be driven, but recovered (at the other parties' expense) to an agreed repairers for assessment and estimates.
I would only inform the insurers if I was going to claim on the insurance, otherwise why bother? As far as I'm aware there is no legal or moral obligation to do so.
As long as the work is carried out to your satisfaction, in a timescale satisfactory to you, then I really wouldn't worry about anything else.
You shouldn't be out of pocket because of this event, and you shouldn't have a vehicle in a lesser condition than prior to it; Everything else is irrelevant.
I hope you get this sorted soon.