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It is likely a good idea to have an independent mechanic at least go to the dealership, assess the damages and make sure nothing is overlooked or intentionally kept from you to ensure that everything is repaired.
Alternatively, you could turn in a claim with your insurance company and have it send an adjuster/mechanic to inspect your vehicle to make sure it is repaired completely and properly.
If the dealership has agreed to cover the damage, this shouldn't cause your premium to increase, etc. as your insurer shouldn't have to pay out anything.