As DrewE mentioned many forget what it is like to have limitd time. While I would agree that the itinerary is too much, you could easily do the northern portion and enjoy it I think.
1 Drive to Mitchell SD or beyond the first day (bad lands are about 550 miles from DesMoines)
2 hit the Badlands on day two and travel farther west to somewhere in eastern Wyoming like Gillette (only 200 miles) just a drive through of the badlands a short hike or two
3 get to YNP get setup etc lay of the land so to speak
4 YNP
5 YNP
6 YNP
7 Teton
8 Teton
9 head east to eastern wyoming/ western SD 450ish miles to rapid city
10 hit devils tower and perhaps something else in the area
11 crazy horse, rushmore, cave park (cant remember the name)
12 travel east stop at minuteman missile monument for an hour or so
13 travel east
the above is just a ball park idea that way you break up the travel days going to and fro if you are ok with driving 600 miles in a day you could easily add a day vacation activities however in an RV that is really pushing it but split the driving it is doable