Sorry to be blunt, but about your diet...
You've seemed to ruled out a hydration issue (and I'd agree that's probably not the case). Something you might want to really consider rethinking is the lack of carbs prior to rounds, and in general. Carbohydrates are the fuel that runs the body. If you (and your hubby) are both on the same diet, that might well explain why you're both wilting in the heat.
Hydration, shade, all the above advice is helpful, but if you don't have the energy in your body from proper nutrition, of course you're going to feel terrible in the heat.
Edit: and by carbohydrates, I'm speaking primarily complex carbs like whole grain pastas, brown/wild rices, etc. Sugar water isn't going to help much.