We stayed at Lewis and Clark Caverns State Park several years back. There are hookups and showers. If I remember correctly the restrooms and showers were clean and well maintained, but we didn't shower there. Not far from there is Missouri Headwaters State Park. The history is fascinating. If she likes caves, she may like this area. There is a campground there, but we didn't stay because we drove up from L&C Caverns.
If you continue south on 287 to Ennis, then West to Virginia City, that is a fascinating area that any child would find interesting. There is a nice RV park in Ennis that we stayed at, Ennis RV Village.