What are you driving? A TV/VCR and a power inverter might be a good investment for the kids.My son-in-law bought both in K mart for about 180.We just finished a trip from Raleigh to San Diego on I-40.Lots to see and three weeks was barely enough,but we traveled only 350-400 a day.Campgrounds are reasonable but getting a shady spot is a problem.Aside from the usual attractions(Grand Canyon,Painted Desert,Petrified
Forest)be sure to see Ghost Town near Barstow,Ca. also Roy Rogers museum in Victorville.Very hot there this time of year (100+) so bring hats and water bottles.Have Fun.
How long are you planning to take for this trip? On the route that you suggest, I could spend more than a year. Some "don't miss" things are Vicksburg Battlefield, Mustang Is. state park near Corpus Cristi, Tx. Grand Canyon, Monterey Bay, Ca., the redwoods, Lake Tahoe, Yellowstone Park, Devil's Tower, Mt. Rushmore, and a whole bunch of others.
Assuming 3,000 miles each way and 21 days to do it, that averages 300 miles per day, every day. That's a lot of driving with kids. Is there any way to scope down the trip or allow more time. I'd allow 3 months for that trip, not 3 weeks.
One of the reasons for RVing is the leisurely lifestyle, but that pace is going to drive you crazy.
I think kids get enough tv and not enough mom and dad at home. Don't let their imagination be compromised on such a wonderful experience. TrailerLife http://www.tldirectory.com/index.cfm has a lot of great car games to play on the road.