I have a friend that just enters a state, then clams they have seen and been in that state. I can not speak about yellowstone as I have not been there. I do know that one can easily spend a week in the SD area. I think you need to pick one go for it and do the next one the following year.
Last year we stayed at KOA in Interior SD. This gave us a good spot to visit, Wall, Badlands etc 2-3 days. From there drove to Custer SD stayed at our favorite spot Fort WeLikit. This gave us great base camp for visiting all the necessary items in and about Mount Rushmore. 4-5 days. Black HIlls Campgrounds | Fort Welikit Family Campground (blackhillsrv.com)
If possible you may want to adjust your plans to stay in the Custer area for the Buffalo round up. This event should be on everybodies bucket list. Buffalo Roundup and Arts Festival | South Dakota Game, Fish, and Parks (sd.gov)
Good Luck
