So OK, I can't comment on the driving part, but when my brother and I were around your kids' age, my parents packed us up and we went (by plane in this case) to the Washington DC area. We stayed with friends. We toured lots of stuff in DC... Smithsonians, the mint, all the usual stuff, and also went up and spent a day in Gettysburg. All really cool sounding stuff, right? My dad was SO stoked to do this trip. But from my brother and I's point of view, we thought the whole thing was super lame, and we argued a lot because we weren't happy. I also think it broke our parents' hearts a little bit that we weren't that into it. As an adult, I'd like to do that trip again. But as a kid, not so much.
So yeah, just something to consider re: making memories, showing your kids Yellowstone, etc. Now, clearly, you know your kids better than us internet strangers, but just really consider if this is something they ALL would enjoy at this point in their lives, or if this is more of a dream YOU have, and they're just along for the ride. My guess is, they'd enjoy it more when they were older (and when you have more time to spend actually enjoying the trip versus driving for half of it).
When I was that age, I much more enjoyed the camping trips we did in the nearby mountains. We had more time to actually hang out and play with our dad (he owned his own business and usually worked 6 days a week), and it was nice to just relax, instead of go go go.
