Yes, The Black Hills are a bit remote but driving does not bother me. I fly alot so I prefer to drive whenever I go for a vacation or getaway. I drove from NE Texas to Teddy Roosevelt with an overnight stop in Grand Isle, NE on the way to Dickinson, ND. Spent about 4 days in that area (ND) and then drove down to Rapid City where I met up with my girlfriend as she flew up for the second week.
We spent the entire second week in Rapid City doing day trips to the Badlands NP, Minuteman Missile NHS, Mt. Rushmore, Custer State Park, Devil's Tower, Jewel Cave, Wind Cave, Deadwood, Spearfish Canyon, Keystone, etc. You can easily consume two weeks just in the Rapid City area if you took advantage of everything to do in the region.
After the second week in Rapid City she flew back and I took a couple of extra days driving back hitting some more NPS sites back to Texas.
Personally, I do not see the need to couple the SD/Black Hills visit with Yellowstone unless you have a lot of extra time to take off. I have done Yellowstone/Grand Tetons separately so that I do not feel rushed.