with kids the same age!
Its really not bad at all! We drove in 07 and stayed offsite so having our own car was great. It saved us a ton of money over flights... even with gas/tolls. (Make sure you have Ezpass)
Last Feb we decided last minute to go to WDW over the school break so flying was out of the question. Only problem was that we got the stomach virus while in WDW so I was out of commission for the ride home and my husband did most of the driving... other than that it was fine.
Our kids are 4,6,8 - we make sure we have DVD player or a laptop that plays DVD's... they each have nintendo DS and games, we bring a cooler bag of snacks/drinks and then assorted books and crayons/coloring books.
We leave after dinner from the NY area (my sister lives in NJ so had dinner there and we left from her house b/c we live on LI) and drive until around 8-9 which is their bedtime. We stop so they can use the bathroom & brush teeth and we get gas or snacks for us. Then we alternate driving / sleeping and by the time the kids wake up we are in GA or FL.
My kids are great in the car, they never usually give us a problem - so that helps a lot! If we stopped and got a hotel room we'd have to do more driving while they were awake so I dont think we would do that. We power up on coffee and books on CD and time flies very fast.
Few things:
1- the 2-6am hours are the worst.
2- the ride down to FL is SOOO much better than the ride home

3- make sure the 4 yr old give advance notice of when they have to use the bathroom, we've had to pull over on the side of the road for him when he waits until the last minute!
4- we consider it a family adventure that they will remember forever!
AND PS our upcoming trip we got RT airfare for 5 of us for around $800 so we are flying!
good luck!