Why does it have to be drive straight through? Drive til midnight. Get a few ours sleep, leave at 7:00 am or so. That would put you in Orlando sometime Saturday evening and you could relax and enjoy the pool, etc and have a good night's sleep. You have already acknowledged that Saturday will be pretty much a write off from being exhausted if you drive right through, so you haven't really lost anything.
Now, having said that, we priced out driving (for us, about 22-24 hours) and factoring 1 night hotel each way, food for 4 people for 4 travel days (we'd bring drinks and snacks but certainly you'd stop to eat at least once per day to get out of the car for awhile!) and gas, it came out to pretty much what we pay to fly, or at least withing a couple of hundred dollars. You know what the commercials say: Not being stuck in a car with your kids for 2 days: PRICELESS.