Best route from Mount Rushmore to Yellowstone National Park?

I'm planning a major roadtrip this august for my family (2 adults, 16 and 10 yr old kids) that goes through many northern US areas and western Canada. However, I need some help along this part:

1. Chicago to Sioux Falls

2. Sioux Falls to Mount Rushmore/Rapid City

3. Rapid City to Red Lodge, MT

4. Red Lodge to West Yellowstone

5. West Yellowstone to Helena, MT

6. Helena, MT to Edmonton, AB

Now, from Rapid City, it's a 7 hour drive to Red Lodge. The reason I wanted to stop in Red Lodge is since it's a close entrance to Yellowstone Park, but arriving in the evening means I won't get to take advantage of the sights of Beartooth Highway. So by stopping overnight, I would be able to travel the route in daylight, and still have time to tour Mammoth Springs. I'd then like to make my way over to West Yellowstone and stay a night there.

The following morning, I'm hoping to cover the Old Faithful Geyser and drive over to the Grand Canyon of Yellowstone. I think I should be able to cover both these activities by 5pm if I leave hotel early morning (9am). I'd then drive upto Helena, MT (5 hours from the site).

MY QUESTIONS- Do you think this is a good plan? I plan on spending 2 full days touring only the major points of interest in Yellowstone, as I have limited time. Does my plan allow me to cover these 4 places well enough (assume both days I leave as early as 9am). I read its about an hour and a half between locations (I said them in the order I'd visit them). Also, are there any points I missed that would be well worth an additional night?

All accomodation, food, route, time, and other recommendations are greatly appreciated! Thanks for your time :)