Details are always kinda sketchy for what is allowed to be brought on base. I've gone to the last two shows, each time with little kids. For what it's worth, I've brought a stroller once, wagon second time. Backpack loaded with drinks, food, snacks and other necessities for the kids. I wasn't given any grief for anything. However, I under-packed tremendously for fear of being turned around.
Website says factory sealed water bottles or empty containers that can be filled on site are allowed.
I'm bringing one of my sons and I'm going to bring my backpack, sunscreen, four sealed bottles of water, folding stool, snacks, camera, hearing protection and FAK.
There are plenty of hotels in close proximity. The only commuting problem you will hit will be the lines for parking. From there, walking and lots and lots of standing in line. Shade comes at a premium. If you don't get VIP seating or find a spot under a wing, or bring an umbrella, you will remain under direct sunlight throughout the duration of the show.