Good for you and William!!! had to laugh as the DH told me "Chief" is taking him on a trip for his birthday next week. We totally get it.
Did you see the recent Adventure Cycling email about new routes in the dakota's not sure if that would affect you as it may have just been in North Dakota
I would HIGHLY discourage you from riding through Yellowstone on any kind of bike in the Summer (sorry) but their are zero shoulders to the roads and traffic is horrid, horrid. (I grew up there) I am not sure what the bus transportation is like these days but it used to be possible to hop on one of the Yellowstone buses. Consider going around the park, perhaps dropping down via the Teton Valley on the Idaho side - driggs, victor, etc. that is a beautiful ride.