Not sure of your exact route, but there are nice lakes in the Ozarks and eastern Oklahoma, all of them have camping and RV parks. Some nice show caves in the Ozarks too... and if you're dropping down to the Gulf Coast, check out the USS Alabama Memorial in Mobile, plenty of parking there in a pretty secure area, outside of town and right on the Gulf. I'm thinking there probably aren't too many battleships to be seen in Nebraska, lol... I don't remember any from my "trucking daze." I would suggest a boat ride or two along the way, that's something else your kids might enjoy, although you have to keep marine safety in mind, especially with really young children. PFDs are legally required for kids in most states, so be sure any boat rental place is up to speed that way. I say this as a lifelong 'extreme small craft sailor' and explorer, lol.
I'd like to make another suggestion, and I say this as a former OTR truck driver: use larger truck stops for refueling purposes, they have separate fuel islands for cars, vans, trucks, RVs, etc., and there's generally more room to maneuver on their larger lots. Plus the bigger truck stops (or travel plazas, as they're now called, since they cater to RVers and other travelers too) are more likely to have security, better lighting at night, more choices in the store or restaurant, more stalls in the bathrooms, all that good stuff. Maybe you won't be traveling at night, I'm just sayin'... and the fuel prices at the larger truck stops can't be beat, they'll be as low as any competition, if not lower. Your (supervised or chaperoned) kids can check out the truck stops too, some of them are pretty cool.
As for other practical suggestions, well, don't forget barf bags for any kids who might get carsick... I still clearly remember my brother Aidan throwing up in a plastic bag while we were on one of our European tours. Right there in the crowded VW Bus, with 10 others watching, lol... ah, yes, those were the days. Some snacks and a cooler for beverages would also be good, you might even buy a thermoelectric cooler that plugs into a lighter jack, those work fine for your purposes and you can store sandwich material, fresh milk, juices, etc., in that cooler---another way to save money. I'm not sure if 'p!ss jugs' would be practical in your situation, use rest areas for that purpose, easy off and easy back on the road. Saves time, ya know? And those kids can stretch their legs a bit, which never hurts.
Okey-dokey, that's all I wanted to add, hopefully you can factor in that info and make your trip a little easier, 10-4? I gave all of my nieces & nephews (20 of them, and now some have kids) the same advice when it comes to ground travel, it's generally safer and the kids get to see some cool rigs too... some of those 'show trucks' are nice, all decked out with chrome and chicken lights, lol. A separate reality for many of my friends and family back on the coast, but still cool, aye? Another site member made a good point, you have half a dozen young kids with you, so overall safety is a factor in your expedition, and I say this as a hand who has seen more than his share of bad neighborhoods and industrial ghettos, lol. Meh, you'll have a good time, think of it as one big adventure!!! CHEERS!!!
P.S. Not to be crude, but my motto when using any public toilet is 'NO SURFACE CONTACT'---just another tip from this seasoned traveler, lol. Not only am I the sole man alive to have sailed a 14' Laser to Los Coronados and landed on all four islands, spending the night at the summits of two, but I'm also known in my own small circle as the crazy fool who sailed a 12' Minifish the length of the Salton Sea, roughly 30 nautical miles right down the centerline of that bad boy. Problem there was: the entire lake is one foul agricultural sump, with heinous shoals of rotting fishbones along the lakeshore. The fish expire in massive "die-offs" caused by algae blooms which deprive the water of oxygen... and the funky ag chemicals don't help much either. Try not to pick such a venue for your boat rides with the kids, lol.
