Stop at the welcome center as you get to wyoming. They are friendly and last time there they had sewer dump available for RV's. One of the few places I encountered in travels. We stayed at the KOA in Casper 2 years ago, fairly nice place few tree's! Time permitting try to visit the Tetons, we think they are much nicer than Yellowstone. Jackson has a great visitor center and is on the boundary of the National Elk Refuge. Good place to visit with or without kids.
If you want a good break stop in Thermopolis to visit the Hot Springs. There is a free one that is a state park and across the street is a commercial one with indoor/outdoor pools. Kids would like this one have water slides etc. Not really out of way the yellowstone, but off instates on state roads.