Hi Paul and welcome to the forum!
We love that area and drive a 40DP so I don't remember there being any real trouble with access roads.
We've stayed at several private CGs in the area but next time want to try to stay in the park itself. One of their CGs inside the park is noteworthy because buffalo roam among the RV sites and you just may have to adjust your plan for the day based on their schedule.
We drove by it and made a note to check it out next trip. I'm sure if you check out campgroundreviews.com you'll find the comments about this in the reviews there.
The Black Hills remains just about our favorite spot among the 34 states we've stayed in.
Best of luck and safe travels.
Rick