If I were coming West from Indiana with two teenagers for two early summer weeks, I would get on I-70 and head straight to Denver. Unless you really like heat, I would avoid southern Utah at that time of year and substitute the mountains of Colorado and New Mexico instead. Drive from Denver up to Rocky Mountain Nat'l Park and, if you are comfortable towing in the mountains, go over Trail Ridge Road to Granby, west on US 40 to Kremmling, south on CO 9 to Silverthorne, and back to I-70. Next stop--Glenwood Springs for the kids to have a great time swimming in the gigantic hot springs pool.
From Glenwood, use CO 133 and US 50 to Montrose, with short side trips to Redstone, Marble, and Black Canyon of the Gunnison NP. If you are brave, head due south on US 550 to Durango and Mesa Verde. If not, use CO 62 and 145 to Telluride, Cortez, and Mesa Verde. Finally, head south on US 550 to Aztec (more Anasazi ruins, but not cliff dwellings) and Albuquerque. Then take a side trip on I-25 to Santa Fe (at 7,000 ft, so normally warm but not extremely hot), then south to I-40 via US 285.
From there you can head home on I-40 through Texas, Oklahoma, Arkansas, and Tennessee. There are many more things to see along the entire route that I didn't mention, but you can find those you are interested in during your own research. And PM me if you would like campground recommendations along any of those routes.