Welcome to the RoadTrip America Forum!
I would say give it at least two solid weeks to be able to enjoy this trip. The round trip by the direct route would be roughly 4500 miles total. That's an average of 6 hours on the road each day for 14 days.
Have you given thought to stopping at Yellowstone National Park, which is roughly along the route you outlined? Have you taken long trips of this nature before, either alone or with your children?