My friend Lynn travels with her kids every other year to California and when the kids were very little she had to change from a "get in the car and drive til you get there" person to taking time to make lots of little stops. She knows the route well from driving it so much but with kids she got a AAA trip planner and found places to stop such as public parks with play equipment, some only had park areas. She also found places to eat such as Burger King and McDonalds that had indoor playgrounds. If you play games or have activities when you leave Tulsa your 2 older kids may be distracted until you stop for dinner somewhere in Arkansas. I would think a movie in the DVD player wouldn't hurt even then for the little ones. After dinner and some serious run around play time getting back on the road and settled down may take a few minutes but the kids should settle down with a movie or something that doesn't require light since it will be getting dark. Also you will have a time change when you cross over into Kentucky from Tennessee. The kids should be asleep by 8 or 9, car travel seems to put kids out sooner because of the vibrations of the car I think.
The times I have traveled from N. Central Ok to Coweta I went up 11 to have more sight seeing stuff instead of constant Turnpike. It took us over 4 hours because I stopped off at parks, convenience stores for walking around, stopping for snacks, etc....I had 2 grand kids, age 1 and 3, my daughter and my Mother. The trip was lots of fun for the kids. They didn't cry or get bored, my daughter (21 at the time) was very bored and wanted to argue all the time so she made the trip horrid for me, and my mom enjoyed being with everyone and tried to make the best of it. We headed back home after a several hours of a swim party. The kids were out in a few minutes of getting in the car. My daughter was out by the time we got to Tulsa, my mom and I enjoyed visiting the next little bit because I drove the turnpike home.
I think you have selected an excellent time to travel due to the excitement of going somewhere and then dinner and then dark and sleep until you get there.
Good luck.