I'd like to know what this costs in the end, including wear and tear on the car if that could be calculated.
Seems like a better way is to rent a truck and a tow trailer, and fly the wife and kids out.
When I moved from Florida to Cincinnati (I suppose right here is where you know I'm nuts!), I bought a used U-Haul 26' truck and rented a tow trailer for the move. I paid about $3600 for the truck, and after I moved I sold it for $3800, so it was kind of like moving for free.
Maybe a risk to buy and own a big truck like that, but I checked it over carefully and selected what I thought was the best one for sale at U-Haul out of about twelve available. They have all the records of when the engine/transmission/rear end, etc. were replaced. I figured it had to have another twelve hundred miles left in it, and it didn't let me down.
No rental time limits on doing it this way, so I could load the truck and drive at whatever pace was comfortable. I also used the truck for storage in Cincinnati until we decided on a house to rent.