OP, you are trying to do too much in to short a period of time and you are overplanning it. After Memphis I would head straight to the Grand Canyon (1400 miles/20 hours) which I would do in two days but it will probably take you three in a C and that many people/dogs. I would leave the dogs home... they are too young to remember all these places even though they sound like they are your children.
I would stay at Circus/Circus's RV parking area. I would spend more time in the Zion/Bryce area and leave off Mesa Verde... another option is to leave off Las Vegas and do Texas/ Mesa Verde/North Rim/Zion/Bryce/Moab and then more time in the Tetons/Yellowstone area.
Some of your driving times are impossible as they do not include lunch, traffaic, and fuel. You need to leave some things off or add another week to your trip. The last part looks pretty good.
