Here is a recent
post that should help with the UT part plus in my second answer some CGs and a route to the Tetons. I've made this trip in a 42' MH. There is a tunnel between Zion and Bryce that's a problem for big rigs. Most will not recommend taking 12 between Bryce and Capt Reef although I have. There are some short very steep areas and it's kind of curvy. These are the only areas of concern all the way to Yellowstone.
If you have the time I'd recommend the N Rim after doing Zion from the west side. 59/389/89A to Jacobs Lake will be 60 miles down and back but then you do not have to deal with the Zion tunnel. There is a USFS CG at Jacobs Lake and a private CG so do the rim in the PU from there. Leave the N Rim just after sunset and see how many mule deer you can count on the way back.
