Louisa to I-81 via route 33 is a road I've traveled many times in a car, truck with boat, or an 18 wheeler. For the most part it's a very good road. Going over the mountain is the worst part of course. I'd say it's not as bad as route 211. The uphill side will be two lanes. Down hill just one. I see lots of trucks use it so I would think most any RV would be fine. From Route 29 at Ruckersville on the eastern side to the base of the first little mountain at Stanardsville is 4 lanes with a median. Over the first little hump is just two lanes but not very many curves. From the western side of the real mountain crossing and on to Harrisonburg the road is 4 lanes with a median. Almost as good as an interstate. The closer you get to Harrisonburg the more stop lights there are.
I'd go that way every time if trying to get from Louisa to I-81.
There's a great BBQ restaurant called "Log Cabin" located just east of the stoplight for Massanutten resort in Penn Laird.