Three or four days won't put a dent in all there is to do and see in the Black Hills. As has already been covered, trying to do the trip in two weeks will mean some looooong days on the road, if you're going to have time to do anything while there.
If you can take the three weeks I'd encourage you to do so. If you can take only the two I'd agree with skipping Wall Drug and the Badlands, but you'd enjoy both. Wall Drug is one of those places everyone should see once, it will only take a couple of hours, and the Badlands are like nothing you've ever seen in the East.
We always stay in the Hill City area (The Rafter J Bar
). It's centrally located to all the attractions and scenic drives. While the campgrounds in Custer State park are beautiful, there are limited sites that will fit your rig, you have to be careful in choosing your route to get to them and it will take you a long time to get in and out of the park for each days outing outside the park. You definitely want to visit the park, it will be one of the highlights, probably on multiple occasions, but I wouldn't stay there. And yes, the kids would probably love the Jeep ride inside the park, although 99% of where they'll take you is accessible by most any vehicle (gravel roads).
Besides the obvious sights, Rushmore and Crazy Horse, the tours through Custer, the needles highway and many other very scenic drives, there are many other things in the area teenagers will find interesting. Bear country (drive through animal park), there's a reptile park, the 1880s train ride originating from Hill City, a couple of caves and much more.
Nope, three or four days just won't cut it.
And yes, if going during the summer, make reservations sooner rather than later, and be prepared for long lines and a lot of traffic in or near all of the tourist areas. When going around Chicago, just plan so you don't hit the city at rush hour and do be sure to take the 290 bypass, DO NOT stay on 90/94 through the central city (the "loop") and it won't be so bad.
You're going to love the Black Hills, one of our favorite parts of the country.