Some of this looks fine, but those 5-6 days in a row of drive, drive, drive near the end may be very tough on your family. Also, be aware that places like Grand Canyon, Tucson and Moab will be hotter than hot that time of year. Yes, I know you're from Florida, but have you really experienced 115-120 degrees in the strong western sun?
You have far too little time in Moab (wayyyyy more than you can see in one day, with 2-3 national parks and a state park in close proximity), Glacier (we spent a week there, and a day trip from Missoula will not allow you anything close to the time it's worth), Yosemite, and probably Crater Lake - again, I'd spend a full day in each one, not just an evening.
If the total time is more than you have available, then knock out a full location rather than cutting down the individual sights. To me, it's a shame to visit a place and leave without seeing all the stuff you really wanted to see.
Agreed. If your family are more interested in what the cities have to offer, then skip some of the national parks. If you are more interested in seeing those national parks, cut out the cities - I'd skip Las Vegas entirely (not exactly family-friendly anyway), and I'd also probably skip SFO and Seattle in order to allow more time for those national park areas. BTW, if you don't have reservations in the national parks, get them NOW - or at least immediately after you finalize your itinerary. Good luck!