Welcome to RTA!
At over 1050 miles from Okmulgee to the Grand Canyon, it's more like a TWO day drive. It's not something that can be done in one day, especially with 3 children in the car. Google maps may tell you that's a 16-hour drive, but in real world, it's more like 22 hours. Google doesn't have to stop for gasoline, food, can't anticipate traffic concerns, assumes you will drive at the speed limit the entire way, and definitely does not have to stop to go to the bathroom. With 3 kids, every stop will take a little longer than you expect.
If you DID try this, nobody would be very happy when you get there. You'd be tired and cranky, as nobody (not even kids) would be able to nap/sleep in the car very well, especially the adults. One adult needs to drive and the other would need to keep the driver awake, so there's no rest for the adult. If you left home at 6 am one day, you'd be lucky to pull into the Grand Canyon by 2 am the next day ... exhausted and ready to sleep, not trying to view the Grand Canyon. Believe me, I know about this. When I was younger, my parents attempted to drive the same distance in one day. They were exhausted.
I would definitely rethink this. Drive one day, stay overnight at Santa Rosa, NM. Stay at a place with a pool for the kids. Eat out. Sleep well. The next day, drive to Grand Canyon, stay overnight. The third day, see the Grand Canyon. On the 4th day, drive to LA - - easily done.
Donna