Vegas will be very hot but not Grand Canyon. It will be warm but not like you're used to in Bama because there's no humidity! :) The nights cool way down.
Definitely try to get a weeks' notice and a reservation at Arches for the Fiery Furnace hike. Your children (& you) will absolutely love it but it's very popular so a reservation is a must. Arches is undergoing a lot of construction all summer so it's going to be slow-going and you'll need a car to drive it. The parking lots there are normally extremely crowded with little rental Class C's and with construction it's going to be a bear. Don't try it with only the motorhome. Plan to head out to the park early morning (even 6-7am) for cool temps and less traffic.