We usually plan on an average speed of around 50mph for planning purposes...That puts your short days at 8.5hrs. Add in little ones and you could easily tack on an extra hour for bathroom breaks, lunch, just letting the run off a little steam. Add in an hour for departure prep and an hour for set up...those are 11.5hr days. By the time you feed the munchkins dinner, it's probably going to be 7-8pm and you won't have any time for touring.
If I'm following correctly, you have 9 nights and 6 long days driving. Presumably the 3 free days would be busy touring...this sounds like a painful marathon. I get with limited vacation time, doing a hard day's run at the beginning and end of a trip just to cover distance but after that, it's really much nicer to slow down.
I think of it this way...
- If you have a great time and everyone really enjoys the trip, you'll probably find a way to do another trip to see the places you couldn't get to and the whole family will be chomping at the bit to go.
- If everyone hated the trip, they will fight going the next time. Sure while they are under 12, if you say they go, they go but they will hate it double...and when they get in their teens, do you want them to try and avoid going with you at all?