From One Aussie to Another.
Hi, and Welcome to the Great American RoadTrip Forum.
Since I am not familiar with the middle portion of your trip, I shall leave that to the experts. But certainly the western and the eastern end are doable. Be aware that the San Diego to Las Vegas leg is a long day in the car, especially for your grandchildren.
At the other end, what jumps out at me is Key West to Naples. Not necessarily because of the distance, but because there is just so much to see and do, that with all the stops, it could make it a very long day. And if you are interested in the Space Centre (between Daytona and Miami), you might like to add a stopover there.
For attractions along the routes, check out the 'attractions' and 'map centre' tabs on the green bar above, as well as this thread.
Just out of curiosity, where are you planning on spending the other 9 days?
Lifey in Melbourne