We will often put in long days at the first or last day of a trip, but not so much in the middle. There are just two of us, and a 500 mile day is a lot. Do you both drive?
BUT, I must congratulate you on spending time in the various destinations you have outlined. So many people would put just one or two nights and then move on. :)
I have made some suggestions below in red. You might find your itinerary is dictated by where you can and can't get reservations. As I note, Yosemite CG's are already sold out in the park, so you'd be staying outside and "commuting" in every day. Yellowstone may also be tough by this point.
Cincinnati St. Louis (1 night) 370 Miles
St Louis Hutchenson, KS (1 night) 461 miles Is there a reason to go to Hutchinson? Stay on I-70 and save some time and distance. When you get to Burlington, CO, head north on US 385 then west on US 34
Hutchenson, KS to Colorado Springs (1 night) 449 miles From Hutchinson, head on I-70 to Estes Park and skip Colorado Springs. It's out of the way, and getting to EP from CS means going on I-25 through Denver. Not a fun drive if not necessary. Estes Park is the side of the park you want to be on.
Colorado Springs to RMNP (3 nights) 168 Miles
RMNP to Great Sand Dunes (1 night) 258 miles Sand Dunes is interesting, but you might also consider overnighting somewhere around Salida. A fun town to explore in the evening.
Great Sand Dunes to Durango (3 nights) 167 Miles Make sure you take the Durango to Silverton Narrow Gauge RR. I'm not a fan of touristy things, but this is one I've done several times. Also, spend a day at Mesa Verde. Make sure you get reservations for one of the guided hikes though a cliff dwelling.
Durango to MOAB/ARCHES (3 nights) 161 Miles
MOAB/ARCHES to BRYCE Canyon (4 nights) 283 Miles Four nights is more time than you need to spend here, given the length of your trip. Spend two nights then move to Zion NP for two nights. Don't try to day trip to Zion from Bryce.
BRYCE Canyon to Vegas (1 night) 268 Miles
Vegas to Yosemite (4 nights) 409 Miles You may end up skipping Yosemite as it will be very difficult to get reservations at this late date.
Yosemite to Sonoma (3 nights) 240 Miles Another option would be to head north and see Lassen NP and Lava Beds NM. There are really fun lava tubes to explore at Lava Beds. Your kids will love it!
Sonoma to Redwood NP (3 nights) 258 Miles Head to the coast from Crater Lake instead of at this point. Take the Oregon coastal route north to at least Newport, then head inland to I-5.
Redwood NP to Crater Lake NP (3 nights) 256 Miles
Crater Lake NP to North Cascades NP (4 nights) 542 Miles There's an awful lot to see between these two destinations. See my comment above about the coastal route. Maybe use those days you had scheduled at Yosemite here instead. The kids will love the coast. Further along the way, you might consider Mt. St. Helens, the Columbia River Gorge (lots of waterfalls), or Mt. Rainier. You might even steal a night or two from North Cascades.
North Cascades NP to Glacier NP (4 nights) 535 Miles
Glacier NP to Yellowstone NP (5 nights) 426 Miles
Yellowstone NP to Devils Tower NP (2 nights) 361 miles As noted, Black Hills might be a better choice. You will have seen so many mountains by this point, you'll know why they call them "hills" ;) )
Devils Tower NP to Teddy Rosevelt NP (3 nights) 228 miles You could give up a day here.
Teddy Rosevelt NP to Minneapolis (1 night) 570 miles
Minneapolis to Mackinaw, MI (3 nights) 510 miles
Mackinaw, MI to Cincinnati, OH
