West Yellow Stone to Casper Wy

Good decision. We've been over all the passes in and around Yellowstone and it's smart to go around Teton Pass. With your route though, it's unnecessary to go that way, but instead through the park, and out towards Dubois, over Togwotee Pass as previously suggested. It's a good road with lots of pull outs for the scenic vistas. Take that route all the way to Riverton, then on to Casper. There's a great campground off Togwotee Pass called Falls. They have two loops that fit all sizes of rigs. One loop is dry camping and the other has electricity as the sites. Both loops are beautiful with nice outhouses. Enjoy your trip.