JJ surely you'll be taking some personal care items with you ... aligners aren't very big, so I'm sure you'll be able to put them in a container and keep them with your personal stuff. Better still ... with your wallet, as I'm sure you'll going to keep in mind where that is at all times.
Knowing when or where you're going to stop, shouldn't be an issue. Keep water, a
toothbrush and toothpaste with you, and you can clean after a meal anywhere.
Please don't turn this into a big issue, as think how many people with fixed braces travel every day/week/month etc ... and we cope without any issues. This year I've travelled overseas and within Australia for several weeks at a time. We've been places where there's no running water, and yet I can still eat and clean, as long as I follow my own rule of having water a toothbrush and toothpaste with me. I carry a travel sized brush and travel small container of toothpaste, plus a small container of mouthrinse ... so it's all very easy to clean, when I'm sitting in a car, bus, plan, train, the side of a salt water river ... or at the beach. Something like this will be as easy or difficult as you want to make it ... please make it easy and do the best for your teeth and the smile you're paying to have.
Good luck talking to your
ortho!