Here's what we usually do when we drive overnight, straight through...
We leave in early evening (usually a little after 5pm). Either me or my wife has taken a couple hours off of work to get everything packed and ready to roll. Then when the other one gets home from work, we're off. My wife does the driving for the first leg, while I try to get a little sleep (emphasis on "try"). Kids get to watch one movie during this stretch.
We usually pack some kind of dinner meal (this year we'll pack some subs), which lets us get a good amount of distance in before our first stop (maybe around 9pm or so). Bathroom break, a little stretching, and then back in the car, and I take my turn driving. The kids usually drop off within the hour and are good til morning. My wife usually falls asleep pretty quick too. Now, I listen to my music or books on cd. All the reststops for the next few hours are related to Mountain Dew or Redbull and yours truly. I get a lot of complaints from my sleepy passengers when I do stop though, so I try to limit this as much as possible (time it with the gas stops).
Then, around 5 am or so, my wife is usually awake again, and we do a quick pit stop to change drivers. We'll go on for another couple of hours and then find a place to stop for breakfast. This is usually our longest stop, maybe an hour and a half. We're usually well into SC or even GA at this point, so we're "getting close"! This prompts my son to ask what state we are in ad nauseum, until we get into FL. To counteract this, we usually put in another movie at this point.
From there, we can usually pull in to Orlando in the early afternoon.
We're generally averaging about 75 mph. This year it will probably be slower with the pop-up behind us (for safety reasons).