I concur with those recommending beer. Nothing is better on a hot day like holding onto a cold Corona all day. We have a beer from Brazil called Brahma, it’s Corona-style but a bit different, give that a try if you’d like.
It’s not that you can’t make cocktails, mojitos are always fun after all, it’s just that with the hotness and the having fun (hopefully you’ve got some game going on, horseshoes or bocce or whatnot), a beer is more portable, less likely to spill, and easier to replenish. Plus you have to make the cocktail inside (or keep replenishing the edible melting ice outside), versus simply grabbing a beer from the cooler.
But if you’re adamant on finding a signature cocktail, I would recommend going in the direction of a large quantity drink you can customize to create your signature versus individual cocktails. I recommend sangria. Add your choices of wine and fruits and alcohol and sweetener and voila, a delicious drink that everyone can enjoy simply by pouring a cup. Plus you can add in other alcohols and fruit drink and wine as the night goes on to keep it flowing if that’s what you wish.