With all of the naysayers on the Suburban, you probably should pass any 3/4 ton or 1 ton gas pickup unless it’s the latest model year with the Ford 7.3 or GM 6.6. Best to go straight to a diesel.
With the Suburban at 350+ HP and 380+ #-ft of torque an HD pickup isn’t going to buy you anything to be safe “towing up the mountains of AZ” as you have stated.
Will an HD truck handle the weight better, sure, but with a family of five and a 7500# GVWR there is t any reason why a properly equipped Suburban (3.42 axle) and proper weight distribution can’t tow that trailer.
If you are looking for room for your kids seriously look at a 3/4 ton or 1 ton full size van. My choice would be an Express/Savana as it should tow that trailer with relative ease and they return good fuel economy when not towing (for what they are!). We used to tow a nearly 33’ camper with seven of us in an Express and it was a great combination.