What are the ages of the children? Have they done some traveling like this before? Dealing with very young kids vs. older kids makes a big difference.
The fact that you are driving a coach may make it easier to do a bit more mileage per day, but I'd be thinking 500 miles per day which adds up to 7 days there, 7 days back. I'd be inclined to put a day off after 4 days of traveling to give everyone a chance to relax and for the kids to have a break. That means 8 days out, 8 days back and 14-15 days at your final destination.
It may even be more enjoyable for everyone if you revise your itinerary so that you are stopping and enjoying more sites and activities while heading west and back east. Do a longer day (500 miles) followed by a shorter day (300 miles or so and stop where there are some things to see and do and take a day off. Then continue in a similiar pattern. Make the trip out and back just as much fun and a learning experience as the final destination.
