I second Terrys, Passport park, so if not in it yet, join, you make back your fees the first trip. Just plan it. Cheyenne west on 80 to Ogden Ut, up 15 and then 20. How many days are you planning? As in miles per day? If you use Ogden as a stop, stay at Willard Bay, SP. Right off 15, Flying J at that exit. $25 a night, FHU. Close to town if you need it, on Willard Bay a fresh water body adjascent to the great Salt Lake. Ogden to Wet Ystone is easy drive, but if you want to break it up, go to Fort hall casino. Not sure about how kid friendly though.
In West Yellwstone, be sure to stop at the hardware store, next to Grizzley RV Park, check out the photos at the register, they are done by my friend Pam. Buy something. (G)
Go to Grizzley Discovery Center, get a nice close look at bears and wolves, these are rescued animals mostly. 2 wolf packs and I think 10 bears. Great learning experience, and kids can go to Keeper Kids, they hide food among the habitat while bears are away, then they can see the bears looking for it. Nnice program.While in Yellowstone, stop at the Old Faithful Visitor Center, ask for Bill in the bookstore. That is me. I may not be there, but that is where I spend most of my short working hours.
Have a great time!