Great advice from Mt. Mama. I will respond to your current questions, as she's answered your original ones thoroughly.
Rushmore Cave cannot compare to Wind or Jewel. IMO, anytime a facility is run by the National Park Service, it will always trump something privately operated. The rangers are well trained and do an excellent job with the tours. I've been to Rushmore Cave, and the tour quality really doesn't measure up to Wind or Jewel. Also, keep in mind that Jewel and Wind are the 2nd longest and 5th longest caves in the world, respectively. That, in itself, is impressive and makes them worth a visit.
Jewel would be the logical choice since you are coming in from WY, but advance reservations as mentioned are a must for those on a tight schedule.
As for hotels, the Roosevelt Inn in Keystone is one of my favorites. I have not stayed there, but others like K Bar S Lodge, also in Keystone. Keep in mind there's no pool for the kids. That could be a deal breaker for you, or you might not mind since I"m sure you might get to swim while camping.
And yes, as Mt. Mama mentioned, it's a shame you have such limited time. An extra night would help immensely, if you could manage it. Your girls would love seeing all the wildlife in Custer SP. You probably would too, for that matter. :)
Please let us know if you have additional questions.