Check for RV parks outside the park near the city of Custer there are a lot of them. We have stayed in Custer State Park but not with our current rig, we just take our tow vehicle and tour the park that way, while staying in a campground outside the park. When we stay for long periods I like having laundry facilities at the campground as ours doesn't have a washer/dryer.
My DH always kept in mind that National Parks have size limits since we like to visit them he made sure we stayed within the limit so we could enjoy staying right in the parks. We have been at Glacier National Park in Montana several times and were allowed only at campgrounds near the edge of the park because anything larger was restricted due to the mountain roads which was strictly enforced. There are campgrounds outside of these usually within a reasonable distance, to us it is just not the same as staying in the park where it is right in the wilderness.
