As most of the others have rightly pointed out, this is too much driving in too little time. First, if you're planning a trip out west, skip the sightseeing in TN, AK, TX and just get west. You have so little time alloted in each of your stops, you won't be seeing anything anyway. Plan another trip to see the Smokies and environs.
Some other comments:
You've alloted a reasonable amount of time for Yellowstone and the Tetons, but you've really shortchanged yourself on some of the NP's in Utah. Even with little hiking, a place like Zion has several days of activities. A trip into Arches is an all day affair, as is the drive up to Island in the Sky at Canyonlands.
Why bother with going to Mesa Verde at all? It's out of the way and you'll get there too late to see anything. Take the extra time in Bryce/Zion and go from there to Moab. Or take some of the days you can save by skipping TN and use one at Mesa Verde. If you do that, don't go to Moab via US 491 but rather take CO 145 up through Telluride and catch CO 90/UT 45 over to US 491. You won't regret it!
You'll need more than one day to see anything around Moab. I'd say two full days minimum and then you won't see much.
Unless you've got something special planned for Las Vegas, why not skip the extra miles heading even further west. When you go from the Grand Canyon to Zion, you can go past Page AZ and see Lake Powell and Glen Canyon Dam.
One more comment: do you think it's reasonable to get such early starts every day with four people and two dogs to get up, dressed, cleaned and fed? And do that day after day? I can tell you we'd be short tempered with each other with the pace you're trying to keep. That's not what I want out of a vacation.
