We've flown to Orlando a few times, driven straight through from Chicago in 22 hours and we've also stopped for the night in GA at a hotel arranged beforehand through Priceline. ($3 a night - can't beat that). In our experience (with 3 kids under 5) it's easier to drive than to fly. Sure, sometimes they whine and we all get a little stir crazy, but try getting three kids through the airport (with carseats, gate check strollers, carry-ons, juice cups, diaper bags, etc.) and onto the plane and you'll see what I mean. Keeping everyone quiet and happy on the plane is a feat in itself. And forget about retrieving the luggage from Carousel A and then trying to board the shuttle bus to the car rental agency - by then I'm ready to cry and go home!
One time we got $59 one way fares on Southwest but, by the time you figured in taxes and rental car, it turned out to be pretty expensive. We could have driven for half that amount.
The easiest so far has been to schedule a hotel stay half way through (GA on the way down and TN on the way back) and hope for the best. Fortunately we've all kept our sanity and we actually have a few "favorite" rest areas along the way. Good luck whatever you decide.