Family road trips can be wonderful! As you know, by the most direct route, this would be a 1700 mile trip and so you would need to cover a very reasonable 425 miles each day (7.5 hours of travel per day). Here are some tips for planning family road trips.
Here are some ideas about places you could consider fitting in on such journey (not all of these would work, of course, but they might get the ideas flowing):
New Mexico; Texas; Alabama; Florida.
Mark