Invitation lists are so hard! I avoided having parties for my birthdays because I couldn't stand it!
Weddings are really hard. We weren't invited to either the wedding of our Best Man's son or our Matron of Honor's son. We were initially very hurt, but in truth, we were not close to those kids. And one of their brides wanted a very small wedding. And for the Matron of Honor's daughters, who I knew more, and whose wedding my friend had more control over, we were invited.
And for one of my Matron of Honor's daughter's wedding, there was a same day cancellation, and my friend asked my parents if they'd like to attend. My parents were thrilled, and I also think it was a non-political choice. She didn't risk asking someone who had just missed the cut.
So, I say, the choice is not whether to go given the late notice, but whether you want to go. Where are you on the desire to go scale and on the obligated to go scale? And if it's more that you feel obligated, examine if you should feel obligated.
I love the joyousness of a wedding. I don't do heat well, but it was worth it for the one I went to. Think about water, hat, fan, cloth that can be wet with water from your water bottle, etc.
P.S. I also spent way too much time stressing about what to wear to that outdoor wedding. I think I was the only one who cared/noticed.