DH and I used to do this every year: either to WDW (once) or Dollywood (many times). here are our tips:
1. stock up on sleep the week before. consider it part of the vacation to get a good 8-9 hours each night. then you'r fuel level is high for the drive
2. make sure the "sleeper" has a seat to stretch full out on with comfy pillow and blanket. when one is driving, the other is getting good ZZZs, not sitting in a seat with your neck rolling from one side to another
3. have an agreement that when one driver is getting dozey, you immediately look for a stop and switch drivers. don't be a martyr--too dangerous
4. in your case, the kids will be in diapers, but we always woke up DS and DD to go potty and stretch their legs when DH and I breaked. They quickly go back to sleep
5. DVDs, etc are a must. I would volunteer to drive in the "after midnight" shift because there is a national radio show out there about hauntings, aliens, etc. that I absolutely loved to listen to...
6. finally, recognize that the drivers will be in somewhat a "jet lag" mode when you reach WDW. Don't have any plans immediately. Check in, settle, and then plan for naptime 3-4 hours in a darkened room no matter what time you arrive. You'll wake up refreshed and ready to go.
Note: we found that the drive to WDW was too long for us and required not only a full day of driving but a day on either end to catch up, so seriously look for regional flights that take you right into Sanford at good rates

we began using Allegient and continue to get seats in the $79-$99 range (each way). Consider it buying an additional 4 days of vacation!
