Having just returned from CusterStatePark/TheodoreRooseveltNatlPark/Glacier/Yellowstone/Tetons/Denver & back to central Illinois.
2nd the idea of staying at Custer State Park, SD for a couple nights, google it & see what you think. We loved the Wildlife Loop - later in the day to see more wildlife. Not sure if any of the campgrounds had full hook-ups (we had electric & water), but it would only be a couple of nights, and the dump station was convenient. Be sure to watch the movie at the visitor center. You might want to see Wind Cave, but get there early to get a cave tour slot (we arrived around 10:30 and had to wait until 12:30 for a tour).
Personally we'd favor Glacier over Yellowstone & the Tetons (as dramatic as they are). If you go to Glacier - we always camp in the park, so no recommendations other than West Glacier for somewhere to stay - Going to the Sun Road is a must, Iceberg Lake hike is nice, the hike behind the visitor's center to Hidden Lake at Logan's Pass is also nice, assuming you don't want to hike all day.
Enjoy! I wish we could have taken our kids at that age to more national parks!
