I've pulled a 35' 5th wheel with a
Smart Trailer attached.
I had the one with 2 wheels and never had any issues with the tires, and we traveled about 10,000 miles before I got rid of it. It worked very well for several years, but I've since gone to a toyhauler and like it better. They did move around back there a lot and I just never got completely comfortable with it. A camera to watch things is a necessity.
I never got stopped but I wouldn't have been surprised to be stopped at some point. They kind of confuse the LEO's because some places consider them part of the trailer. A motorhome pulling a trailer probably would be the best idea if you're enamored of taking a car and bike both.
I've not seen any campgrounds/RV parks with attached garages. There are portable bike cover type things, and actual bike covers that work well enough to keep the dirt off. I mean it's a motorcycle and they get dirty.