If your car is leased, I think you should goto the same dealership for the repair, so they can't give you any hardtime on this when you returning your car at the end of leasing.
Your insurer shouldn't have any problem with fixing the car at the dealership.
Full coverage = repair then deal with responsibility
Basic coverage = deal with responsibility then repair.
In case of lease, it's full coverage for sure. So contact your insurer asap. Let them give a list of bodyshop. They will also pay for the car rent, just ask for it.