We just did the NJ to HHI drive three weeks ago (w/kids - 9, 6, and 1). We also figured on 12 hours and a one night stop. I also recommend the Hampton Inn is Santee, SC. Very clean, etc. Wake up the next morning and you're less than 2 hours from HHI.
The first day drive was a lot longer than we expected due to traffic in Northern Virginia. We left very early in the AM (Saturday) and hit no traffic at all through Baltimore, DC, and the Springfield Interchange. Then it just stopped! It was a mess until we got to 295 and went around Richmond. Smooth sailing from that point forward. On the return trip again we had no problems and then just north of Richmond we hit our first traffic-jam (accident). Not wanting to face further problems, we took the 301 alternate (to Bay Bridge, MD's eastern shore).