We have found September to be a good month for vacationing. Families with kids are back at school and crowds are lessened. However, that said, we were surprised by how crowded Yellowstone was even in mid September. We did get a bit of snow one day, but the rest of the week long stay at Yellowstone was beautiful, mild weather.
I agree with several other's responses that you may have too ambitious of an itinerary. Pick one section (Yellowstone/Black Hills/Devil's Tower maybe Glacier) or (Utah/Arizona/New Mexico) and go with that. Yosemite is really outside of both of those groups unless you have much more time to spend on the road.
I also agree with Lauren. If you are just looking to check places off on your list, you can spend a day here and a day there (and lots of days driving) and get them all in. If you want to actually experience the natural wonders of our beautiful country, you will need to slow down and spend some time. We always plan for a day off every now and then, to spend in camp, sleep in later, cook a good meal, and sit around the fire. Especially at Yellowstone, your days will be long and you will get back to camp later in the day and not want to begin meal prep at 8 PM.
Just my thoughts for you to consider or not. Whatever you choose, have a great adventure!