Having done a lot of trips like that during the work years I would spend the first couple of days heading out of town just burning up the miles to get away from the home territory. Then slow down and starts smelling the roses as they say.
Personally I wouldn't plan on too much time right at the Grand Canyon South Rim but you might check into including the North Rim which is basically a half day's drive around from the South Rim to get there.
Plan out one route going and another heading back home and do some homework of sites along the way that would be of interest to your family.
A personal favorite of mine that might be of interest to your kids is Meteor Crater a few miles east of Flagstaff. And there is a nice little campground there too but not with much to do for the kids though.
Good luck with the planning and happy travels.