A few thoughts on your current plans:

Minneapolis remains a fair bit out of your way, and you won't have much time there on your current plans, but Buck and myself have both already mentioned that.

If you want to get to a rodeo in Cody, then I'd spend at least the last night of your black hills stay in the western black hills, somewhere like Spearfish or even into Wyoming. It would likely make more sense to do that anyway if you want to visit places like Deadwood or Devils tower that would require a lot of backtracking if you stay only in Rapid.

Rather than Cooke City, which is actually the northeast gate of Yellowstone, I'd look at spending that night in Gardiner, which is much closer to the main loop road. Cooke City would mean going all the way out through the Lamar Valley. I'd say your Yellowstone trip would look like this:

Day 1: Drive by the lake, See the mud volcano, Canyon, and Tower Falls areas, heading briefly into the Lamar Valley if you have time (I kind of think you won't).
Day 2: See Mammoth Hot Springs, Norris Geyers area, and as much of the other geyser areas between Madison/West Yellowstone and Old Faithful as you can.
Day 3: Finish the Old Faithful area, and if time the West Thumb area before you head south to the Tetons.

Here's a look at some of the many options for things to see and do along I-80, although if you are going through Denver, you might also consider I-70. Check out the Map Center for more ideas for things to do along both.