Lots of great suggestions here and I concur with just about every one of them. Utmost importance is the children's safety. If this is your first visit to Yellowstone and I assume it's theirs, also; patience will be your best friend. The animals don't use a time clock, the geysers aren't on any schedule but their own. You may have to wait a while for an eruption or for a herd of elk or bison to appear. What do you have in store for the kids to do while you wait? The Junior Ranger program is excellent. If you have an inexpensive digital camera, let them take lots of pictures. Bad shots can always be deleted. Knowing some history of the park can also be entertaining. For example, the U.S. Army was stationed there to protect the park before the NPS was created. The original barracks and stables are at Mammoth. Imagine patrolling the park, about the size of Connecticut on horseback before there were roads. Now imagine doing the same patrol during the winter. (We've been there twice in the winter.)
I assume that you have a dinghy for transportation. Tower Falls and Beartooth Pass are worth a trip if time allows. My wife and I spent five days at the West Yellowstone KOA and we saw enough to say we were there, but left enough that we'll have to go back. I believe you feel the same way when you pack up for home.
