On road only unfortunately. Won't be doing any camping. We have a cabin.
Got it. I also realized that you have more than ten days available, which is good.
Near SLC you should visit Park City. Your wife will love it and there are several very scenic, good roads leading to and from it. I know of one state park on a lake that rents cabins and Yurts and there maybe more. Let me know if interested and I'll plot a route for you.
From there, take I84 and I50 into Idaho and towards Grand Tetons. Even the interstates are pretty scenic there. You can take a coffee break in Ogden, which is a nice, smaller town. I'l let others chime in about the details around Grand Tetons as I approached this off the paved roads and camped there.
Yellowstone is going to be challenge. There are a ton of great dirt roads around the park with beautiful camp sites. But if you do not have a hotel/motel reservation at this point you will have to stay further away from the Park and make a quick dash in the morning. The entrance close to West Yellowstone is by far the most busiest. I would enter via one of the other exits and then leave towards West Yellowstone, which is nice for dinner.
My most memorable Yellowstone visit was a self-guided snow mobile trip with wife and a group of friends. There is a
lottery in August for the few permits (5 sleds, 10 people) and I was lucky to snag the $40 permit in December while living in Bozeman. Some people cancel as the winter approaches and their permit become available again. So, even if you strike out in the initial drawing, keep an eye on the
web site.
Imagine a landscape under several feet of snow with steam, hot water, and bubbling mud coming out of the ground. Partially frozen waterfalls, Bison with frosted mane, and watching Old Faithful while sharing snacks in bulky coveralls. This trip was physically demanding but several folks were moved to tears by the sheer beauty. It is a great way to escape the summer crowds. You can fly into Bozeman and a rental car will take you to the North entrance in less than 2 hours. Snowmobiles and gear can be rented there for what I found to be a fair deal.