Hey everyone!! Here's my .02.
We drove it from Houston 3 years ago -- headed out by 4:00 a.m. and made it to Pensacola by 5:00 p.m., that's where we crashed for the night. However, after eating dinner we thought we could've gone on and finished off the trip. Next time, which is not until next summer, we'll go all the way in one shot. The total drive time from Houston to Disney for us was 17 hours, of course DH has a lead foot.
I have no idea what the traffic, road construction or any other troubles may be currently. Our last trip our kids were 18 mos, 13 and 10 -- everyone was fine, lots of video watching -- the baby did a lot of sleeping and it just so happened that everytime she woke up it was time for either gas, potty or food - and then she wanted her Bear in the Big Blue House.
BTW, we did stop prior to Pensacola so that my dad and DH could do some gambling in MS - I think we stopped in Biloxi but I don't remember -- mom and I took the kids to a park and did a little souvenier shopping on the beach while the guys gambled. Whatever you decide, I'm sure it'll be perfect for your family. Also, we started our trip from Jersey Village - just outside of Houston.