Welcome to the DIS.
We like to leave early in the morning, around 5 am. The first day we like to reach Charlotte, NC. That's around 13 hours of travel time and we're just north of Toronto. The second day is shorter. We typically reach Orlando around 5 pm. In the past we have stayed off-site that night and toured DTD but now that we own DVC we'll stay on-site.
We have two kids too (DD9 and DS7 now but they were 7 and 5 on the first trip). We try to stop at the welcome centers. They have enough open space that the kids can run around. We pack breakfast and lunch for the first day. We eat breakfast while driving and lunch at a welcome center. We try to minimize all of the other stops.
We do pre-book a hotel. Others stop at the welcome center and make a reservation there or try their luck with coupons. If you aren't confident about where you will reach then make a pair of reservations about one or two hours apart and cancel one of them when you get close to the first. Most hotels don't charge if you cancel by 6 pm.
The mountains through Virginia and West Virginia are amazing. There are a number of lookouts that you can stop at and take pictures. As well you will go through two tunnels. We're still trying to get that perfect driving into the tunnel picture. The rest of the drive isn't all that scenic but there are places to stop along the way. The exception is Georgia. I95 seems to miss everything through Georgia.
The trip back is different. We leave WDW around noon and drive to SC/GA border. The next day we drive to Morgantown, WV. That leaves around a six hour drive home. We have often thought of planning a day trip on the way home but nothing seems interesting after WDW.
One neat thing about this route is how many states you pass through. We always put together a small surprise for each border crossing. This lets us dole out treats for the kids and have them looking forward to the journey. The surprises are all small (glow sticks, disposable cameras, books on cd, travel games, ...). We make up a copy of the route for the kids to mark up and track where we are.
Here are some links to other driving threads:
http://www.disboards.com/showthread.php?t=1015289
http://www.disboards.com/showthread.php?t=1014683
http://www.disboards.com/showthread.php?t=1005718
http://www.disboards.com/showthread.php?t=1005273
http://www.disboards.com/showthread.php?t=884576
http://www.disboards.com/showthread.php?t=852050