Whoever you choose. Yourself, RV shop, autobody repair shop, car dealer.
Last one I did, it was me. 2012 Honda Fit, BlueOx baseplate. It took me 10 hours work over three days on a concrete driveway in 100+ F weather (4th of July weekend). Took so long because I probably needed 4-6 drill bits to drill the two holes, rather than the one bit I had.
It is problematic. Some cars need a lot more disassembly than others. Body shops are pretty good about this part, but may have no baseplate fitting experience. RV shops may have more baseplate experience, but your car might be new to them. To help, both Roadmaster and BlueOx provide pretty good instructions as to the disassembly of your car, installation, and reassembly.
Service department of your car dealer is probably not a good idea. Some of these installations require doing things prohibited to auto dealerships, like permanently removing mandatory safety equipment (bumper bars, associated air bag triggers).
Preview the installation instructions before deciding. In my case, I looked at BlueOX and Roadmaster, chose BlueOx because it left Honda's bumper in place, although I had to drill two holes in the subframe and enlarge two more, and remount the bumper. The Roadmaster solution simple eliminated the front bumper and mounted towing brackets in its place, something I didn't find satisfactory. In both cases, about an hour's worth of work was removing and replacing cosmetic body parts covering the front end structures.