I made the mistake 31 years ago of staying at a motel in White's City. I doubt I would ever try to stay in their RV park without visiting it first. The reviews say it is getting better. I will have to see.
Yes, the hour to hour and a half long drive each way is a pain and will be a challenge for the youngster.
Do go online and book 'tours' soon. I would make my first day a walk down the natural entrance after arriving about 1-2 pm. A light snack in the Big Room, then the circle of the big room, dinner at the café in the Visitors Center and the sunset bat flight. Might have time to drive the circle loop before the bat flight.
For a second day - I'd book the 9AM Left Hand Tunnel tour - kids seem to like the candle lantern tour. Lunch in the Big Room Cafeteria - then the 2 pm King's Palace tour to finish the visit.
Be sure to have appropriate jackets and maybe even gloves. It is cool in the cave and you will be in it for several hours.
Actually white cotton gloves are a good idea for the kids - because they are supposed to not touch anything. Fingerprint body oils will stop formations from growing - there are many examples of this damage. If the kid accidently touches something with white cotton gloves - the damage is minimized.