Thank you all very much for the feedback. I've made the following changes to the trip planner based on it :
1) Added 2 additional nights in Yellowstone (one at the Lake and one at Gardiner) and rejigged itinerary to spend more time between stops.
2) Moved the Cooke City stop to Red Lodge - will do Gardiner -> Red Lodge as a leisurely day drive.
3) Bypassed Billings altogether - will go Red Lodge -> Bozeman
4) Added Two Medicine area in before finishing the day at East Glacier Village.
5) Spending additional day in Glacier area.
6) Bypassed Missoula altogether - will go Whitefish -> Couer D'Alene
7) Added an overnighter at Moses Lake so can do the detour to Coulee Dam on the way from Spokane.
Also thanks for the suggestion to get on the road early at Glacier - won't be a problem, we're early starters.