Welcome fellow RI'er! I've made the trip twice alone with the three kids in April. The first time was an absolute breeze so we decided to do it again the following year. To be honest the cost factor about equalled out.
Rented a car-$141 for 10 days (an absolute freaking awesome deal);
hotel in NC for the night ($100 each way);
GAS (huge expense)
small snacks when we stopped (I did bring lots of drinks and snacks but somewone always wanted something different
Misc. things to keep them occupied on the way down (window markers, coloring books, some arts and crafts (silly me)
I would suggest giving the DVD players to the kids as an X-mas gift! Rent movies are redbox, there are plenty along the trip
We left RI about 3:00 a.m. and drove through to Lumberton,NC which is right on the SC border. Woke up about 6:00 am. and got back on the road-beleive we arrived in Orlando about 2:30p.m. And that was only because I got off EVERY SINGLE EXIT looking for a Dunkin Donuts

FYI. You won't find one until FL!
If you have any questions feel free to ask
PS: I highly recomend purchasing the book "DRIVE 95" its full of useful tips and breaks each exit down by what services (Burger King, McDonald's, Dunkin) are at each exit. I bought mine at Borders