We just got back from a trip to Fort Myers, FL (from Cleveland, OH) and we drove. We have 3 kids (5, 3, and 10 months) and my Mom went also. That was 6 people in our Honda Odyssey and it worked out very nicely. We drove straight through 23 hours, because it's easier for us to just keep going (and definitely much cheaper than flying). Also, it gives us a vehicle when we get there. There were 3 drivers and we just switched off and the kids slept fine at night. We left in the evening when we started the trip. On the return trip, we left in the morning. It worked either way - we changed it up to accomodate our schedule. Our DVD player was invaluable and the older kids had activities and toys in their travel bags. The kids have all been on long distance trips since they were infants, so they really don't know any different. As far as all the suitcases and "stuff" to take, we have a large top carrier for our van which is great!
A fun place to stop that I haven't been in more than 20 years is Chattanooga, TN. There are good attractions there - Rock City, Lookout Mountain (you can see 7 states on a clear day), and Ruby Falls (in a cave). I remember my brothers and I really liking this place.
I hope my experiences can translate to your kids and needs for your trip. Have a great time and good luck!