I drove home from Savannah to Boston in March, took about 16 hours but I didn't have the kids with me. I've done 15 hour drives with my 3 boys so what you have planned isn't that crazy.
Two things for you to keep in mind - you need to time your trip so that you miss the Baltimore/DC area during the morning rush. Not sure what day of the week you are going but if it's a weekday you'd be hitting that area at a bad time. Also, the only two cities you're going to hit in SC are Florence and Santee. If you don't make it to Savannah there's not a lot of options for places to stay outside of those two clusters.
Personally, I like driving at night with the kids on long trips like these. A sleeping child doesn't ask "are we there yet". Good luck and have fun!