I did a five week trip hitting Black Hills, Yellowstone, Salt Lake City, Canyonlands, Arches, White Sands, Carlsbad Cavern, Vicksburg, then back to SC. So four weeks for a Yellowstone, Dinosaur, Bryce, Zion, Grand Canyon back to VA would be nice. Or take four weeks and just do Badlands, Black Hills, Yellowstone, Rocky Mtn National Park and you will have lots more time to get away from the pavement.
Try to go as early as you can as the later you go the hotter and larger the crowds.
To plan your trip, use any mapping program to figure out where you want to go. However, don't rely on time, but use the miles and figure an average of 50mph. This gives you time to make potti breaks, eat lunch, fuel stops, and a little sightseeing. Also, plan harder drive the first day out to get out of your usual camping area, then slow down. I try to figure stopping about 4 or 5 so if the day goes longer by an hour or two, not a bad thing.
When we had kids, every other day, we also tried to stop someplace with a pool as it was a great way for the kids to burn up the stored up energy from traveling all day.
Lastly, make the kids part of the team. We traveled without reservations, so I would let the kids look up the campgrounds for the nights stop in the Woodalls. They also had their own map and atlas so they could follow along and help figure out where we were going. This also added to the excitement for them as if they saw something they wanted to see, we would explain the consequences (more travel time or missing something else) so it was up to them to help decide. They didn't get their way all the time as we had final say, but they got theirs most of the time which made the trip much more enjoyable.
Another advantage of no reservations was we didn't have to detail plan and could change on the fly. Like when we stopped in Robinsonville State Park only to discover they had a nice indoor pool for the evening exercise, a true stage coach ride (take one if you ever get the chance!) and then a horse back ride up to a bluff looking back down over the fort. If we would of had reservations, we only would have been able to use the pool. Some people need to know they have a place to park for the night and it also depends on the time of year if you can go without reservations.
One other advice, don't forget to figure in a day here and there for restocking and doing the laundry. NPs aren't the best places, so we almost also stopped for 3 hours in a town to do the grocery shopping and laundary.
Have fun and enjoy. Don't try to over plan and take the fun out of the trip.