Yes there is a lot of driving to get east and west. We live in NM and I drive every other year or so to visit family back east.It's an awful lot of driving to get out west. Is there a place in Missouri/Oklahoma that you would recommend staying for an overnight (or a couple nights to break up the trip)?
I'd like to answer this from the point of view of the parent who's in charge of packing! Sounds like you'll be hitting many campgrounds along the way. That means lots of setting up and tearing down. And packing, unpacking, repacking, answering questions about where things are packed, etc. So for me, this depends on the age of your kids. If they are old enough to be responsible for their own clothes and toiletries and to help (like actually help, not "help") with cooking and cleaning, then sounds doable. If they are little or not good at helping, then honestly it sounds like a lot of work for you & spouse.
We are going on a non-camping roadtrip in a few weeks and this will be the first time I'm making the kids pack and be responsible for all their own stuff. Hoping it goes well so we can consider longer PUPing trips like yours in the future!