I have on my Cabin car, and also have on my other campers/cars, an agreed/stated value policy.
It requires an appraisal and photos, and if something happens, they pay up to the amount.
Never had to use it, so I don't know how good it is, but it is far better than having a problem, and letting them
determine the value
As far as who you take it to for repairs, some trailers could be fixed by an RV shop, but many others would quickly be totaled after the ins. co, figured out how much effort would be required to repair it.
I'm not an insurance expert, but generally, the "coverage" you get when towing the trailer with your car, is only for liability.
That doesn't cover damage to the trailer, only damage caused
by the trailer.
This is one of those times that you should seek out a pro that can give you answers backed in writing...