We always drove straight through when we drove, we wanted to get there and cut down on budget costs! We opted to drive last May, there were just 3 of us adults, and once I figured in extra meals and hotel and days off work to stop and stay somewhere it ended up being just as expensive to fly! So we drove straight through.
Now, last year we drove from San Marcos, so we went south through Houston and across through Baton Rouge and such. It was a piece of cake! I would not have wanted to stop, either. From start to finish, including meal and potty stops, it was just 17 hours. We left at 10pm and got there early afternoon the next day. Nightime driving was the best - no traffic, no obnoxious drivers, no construction, etc. Great! Daytime was more frustrating as there was more traffic to deal with, even on a Saturday. We also needed to just get 2 meals this way, breakfast and lunch. We had dinner at Pop Century =)
When we were kids and drove straight through, mom and dad made us go to sleep and put us in the car asleep around 11pm and dad drove all day long. By the time we were awake, most of the trip was over so we didn't go stircrazy at all.
For us, driving was easy and worth it. This past trip we flew because it was just DH and I and he can't drive long distance or at night - he knows his limits thankfully. I ended up driving the majority of the 17 hours last year and was fine with it, and knew I could do it. My sister stayed up to make sure I stayed awake and okay.
I think if you stop after 13 hours, you might as well push that extra 4-5 hours and just get there, but everyone needs to learn their limits and judge accordingly. Lots of people cannot do nighttime driving, and it's good to realize that and drive in daytime only - even if it means 2 days of travel and a hotel room somewhere in Mississippi. If you want to stop and break up the trip, I'd do it more halfway than that...
Good luck in your plans!