We did the entire Blue Ridge Parkway and Skyline Drive in 2017. We found RV campgrounds within easy distance of the Parkway and left the fifth-wheel in camp. We selected "base camps" roughly 100 miles apart
On the parkway, we found that 50 miles one way and return was a about right for one day, since you want to stop frequently at viewpoints, and to spend time at some of points of interest. So we spent two nights at each basecamp. From mile zero of the Blue Ridge to the north end of the Skyline, we used four base camps.
As to taking a trailer on the Parkway, you may find parking at some viewpoints to be limited or impossible with a trailer.