How do you define best route? Even with 2 points, the goal is not clear. Shortest distance, fastest time, best views, easiest for a mega-rv? With multiple points that could be traversed in any order the choices go up significantly. How about overlaps and cris-crossing? How about seasons? Northern parks might not be open in the winter, southwest might be too hot in the summer.
Mathematicians have what they call the Traveling Salesman problem. It's an abstraction of this issue - how to visiting multiple points with a minimal 'cost'.
Rather than trying to 'optimize' a national trip, consider focusing on different regions. Utah is practically a region on its own. Hawaii and Alaska each require special trips. You also leave the RV behind to visit Isle Royale. Oregon has only one, which can probably be combined with a northern California trip (or possibly Washingon, with 3). There's another cluster around Washington DC. Each has its own optimal season.