Alternatively you can get the train, The Overlander, which runs 3 times a week. It leaves Melbourne at about 8am and gets into Adelaide about 6pm, no hassle, no need for an overnight stop, plus you can watch the scenery from the window.
There are 2 classes of seat, the cheapest is $90 adult, $45 child
The more expensive one is $134 adult, $90 child
Driving long distances in Australia can be fairly boring, plus you have to watch out for the police, your children might get fed up being in the car for so long and you may be jet-lagged, so plane or train would be less hassle. Driving at night can be a problem with animals straying on the road, I don't know whether the road to Melbourne gets many kangaroos but they love to jump out in front of the car!!