When I camp, I hate staying only for an overnight. All of our trips are at a minimum two nights at a site. Even with two nights, you really only have one day there - the day in the middle, as the arrival and departure days are taken up with, well, arriving and departing!
Honestly, with kids that young, are they going to enjoy those national parks all that much? When our kids were below 10 years old we went mostly to "resort" style campgrounds with lots of things for kids to do. As the kids got older we started to go to less fancy (and far less expensive) campgrounds and started exploring the area and historical sites.
Having said all that... it does sound like a good trip, and you know your family, so if it fits then go and have fun!