LOL!
I agree with the "just bring the potty on the sidelines" theories, and I was going to suggest a kids pop-up tent as well, if needed.
If it makes you feel any better, my youngest, at 2 1/2 started hollering to go potty, -immediately- after we dropped my husband at the airport. So I whipped over to the side, and brought her to the hatchback to use the "travel potty." (I LOVE my one-piece Baby Bjorn, and a friend got an even better one at IKEA. You just drop a disposable diaper in it to catch everything, then wrap it up, just like you used to.)
So, here we are, parked in front of a sign that says as big as Dallas, "NO PARKING". . . one of those security dudes comes at me with a whistle. . . as soon as I stepped aside and started to explain that "when she's gotta to, she's gotta go," he dropped the whistle, turned, and practically RAN back to the terminal. :-D
Best of luck. It sounds like you're doing great!
M.