I'm from Wisconsin (an hour north of Milwaukee) and drove this past September for the first time. We're in a different situation than you since it is just my wife and I, so we don't have to worry about kids on the long drive. However, and again this is just me, I LOVED the drive. And I'd never be without a vehicle again in WDW after this last trip.
We drove about 14 hours to Morrow, GA on the first night. Stopped for the night, and drove the last six or so hours the following day. The cost was about a push compared to flying. And that's for two of us. So my guess is you'd come out ahead in that respect. But again, different situations. We were able to take a smaller vehicle, which gave us better gas mileage. If you rent a van, you might only get 12-14 MPH where we averaged closer to 26. We only had to get one hotel room on the way down; you may need two rooms to fit all six of you.
My advice (simply because this is what I did) is to start with the cost factor. There are a few websites (I think
AAA is one) where you can enter your type of vehicle and to/from locations, and it'll calculate approximate fuel costs. Then figure ~$100-200/night for hotel on the way down and back (depending on how many rooms you'll need), cost of snacks and meals, and anything else you think you'd spend on the round trip drive. And compare that to the cost of the flight, airport parking, meals at the airport, etc. and see where you come out ahead.
Like I said, it was about even for us. But I was also pretty excited to try driving, so that weighed into my decision. If your costs come out close, then you have to decide how much you really want to drive. For me, I found driving to be a lot less of a hassle than flying. But I also hate the airport security checks, worrying about the 3-1-1 liquid rule, gate changes, delayed/cancelled flights, luggage weight, and so on. I also know a lot of people who think those are minor inconveniences when you can board a plane and arrive at your destination 3 hours later instead of driving for 20+ hours. Different strokes for different folks.