Spinner,
We drive from West Haven, CT via I95, the last Friday in July every year. We've found that if we leave at midnight, not only do the kids sleep for 7 or 8 hours, but we can get all the way through D.C. before rush hour. DH and I trade driving every 3 to 4 hours then stop for the day in Walterboro, SC. There is a very nice Holiday Inn there in which we stay every year. (Ask for the 2nd floor facing the pool) We arrive around 1pm or so. We all have a long relaxing swim (there's nobody there at that hour!) and a good dinner and get to bed early. Next day we wake up at 5:30 a.m. (Holiday Inn has a very nice breakfast included in the room cost, not just a continental) and get on the road as soon as possible. We arrive in Orlando between 11:30 a.m. and 12:00p.m. I think we have it down to a science. A week later we come home, leaving around noon on Saturday. We stay in Lumberton, North Carolina, also at a Holiday Inn on the way back. The only traffic we hit the whole way is on the George Washington bridge coming home. We always hit the bridge around 7 p.m. on Sunday and there's always traffic. However, being from Long Island, you won't have to cross the bridge!
Have fun and be safe!