"A little further" than Amarillo is going to put you about another 40 miles and Dumas, or 75 miles, and Dalhart. Nothing really due west on I-40
Though I heartily disagree with those who want to intentionally skip one of the most iconic sites in Texas because of a little heat. I will bless your skipping of the musical Texas
It does run pretty long, and then you have to join the line of traffic climbing the single road out, after the performance. Add to that the fact that we are in a hot spell, it ain't the best time. And I suggest a dedicated trip, with time to explore the canyon, and also take in the PPH Museum in Canyon, Caprock Canyons, and other sites. Maybe save it for when you are only going to Newer Mexico.
I have only been to the windmill museum for a quick trip, I recall it was pretty decent, especially for a fan of windmills. The disadvantage is that it is on the lousy side of Lubbock, not much in the way of restaurants etc nearby. Though you aren't too far from prairie dog town, if your kids want to see that.
Also, isn't Lubbock off your planned route? Again, maybe plan it for another trip, and include the Ranching Heritage Center, which is a very good museum. Lots of old farm and ranch buildings.