San Antonio, TX to Yellowstone/Mount Rushmore

There's not much to see between SA and Mount Rushmore without going out of the way. My suggestion is to get up to South Dakota as rapidly as possible (Mt. Rushmore is about 1260 miles for you) then start sightseeing on your 3rd day. Heading westerly out of South Dakota to Montana I got a kick out of seeing the Little Big Horn Nat'l Monument. It was quite a history lesson sitting on the porch of the visitor's center and having the ranger tell the story of Custer where you could see the terrain. It's fairly easy to make it over to Yellowstone from there and you can keep the kids occupied for 5 days there easily. From there I'd suggest going by dinosaur Nat'l monument in NE Utah and the Rocky Mountain Nat'l Park in Colorado. They would probably like seeing the things around Colorado Springs or might get a kick riding the train from Durango to Silverton or checking out Mesa Verde before heading home.