Make one kid become navigator. Plan the route to include something interesting. Another will be responsible for finding a good campground on the route for mid-trip spots. The other responsible for finding meals within the budget requirements.
Make sure the kids have an input on the destination and route. Use the trip to teach them budgeting.
As you well know, most of Texas can easily be in the 100s in the summer. Durango is a great destination, but the mountains of New Mexico are closer. Red River has a lot of activity for kids and adults. Ruidoso is a good base for exploring around.
I personally like the Ouachita mountains and lakes of Arkansas/ Oklahoma, but it is better weather wise before Memorial Day and after Labor Day - which won't work with school age kids.
One activity which might be interesting is caves in the Texas hill country. Warm outside, but cool inside and several caves are around the area.
Personally I'd choose Inks Lake SP rather than a COE campground, because you will have swimmable water in that lake. Guadalupe River and Perdernales Falls State Parks have nice wading / splashing water. And you can get to Schiltterban in New Braunfels.