One thought about Wyoming: Don't let your guard down. Wyoming is a tough place and can really punish you.
My kids went to college there and we've had more than one misadventure.
The unexpected snow isn't too bad, because you can see it coming and it's not too hard to hunker down somewhere until it's over.
Last September we had a day with heavy winds that surprised us. At one of our fuel stops, my wife discovered that the wind had blown one of our bedroom windows out. The window wasn't cracked or broken; it was just plain gone as if we never had one. We had to stop at Walmart for plastic & duct tape to seal it up in the rain for the rest of our trip. Brrr.
The distances are deceiving too. Although I-80 and I-25 are wide and fast, the rest of the highways are smaller and slower and you really have to manage your fuel stops.
We've had more than one crazy detour because of seasonal road construction. Like the locals say, there are two seasons in WY: Winter and Road Construction. One day going from Laramie to Casper we followed our local friend on a detour to beat the construction stoppage. We took a dirt road over the hills and ended up driving through Dick Cheney's ranch. "Wave to the nice woman in the khakis and the blazer with a bulge on her hip. She's from the Secret Service."
Since you're already going to be in the Black Hills, I would try to add the Devil's Tower to your trip. We've been to the Tetons and to the Devil's Tower and we enjoyed the area around the Devil's Tower better. They're both great, but we enjoyed the drive up in the northeast better than the west.
Anyway, sorry you can't squeeze Seattle into your trip. :B