I take my DYH out to festivals in the summer - he's even been written up in the news. Warning: walking around a crowded festival, particularly one with lots of children, often means being mobbed. You walk a few meters, have to stop for people who want to see him, walk a few more meters, have to stop again....
When we're outside, he's in a flight suit or feather tether. Actually, come to think of it, it's been a while since I last used the feather tether, I usually just opt for the flight suit these days.
In the car he's very unhappy if he has to be in a travel cage, even though that's easiest, and he'll complain quite a bit. He wants to be able to roam freely, usually sitting on a shoulder, often a preferred shoulder. Sometimes he doesn't want to be high up though. When he moves around it can be a distraction to driving - I've even had two occasions where he tried to climb down to near the gas and brakes(!!). But usually he's well behaved.
Concerning pooping: he's potty trained. Unfortunately, that means "potty trained in normal circumstances"; the less comfortable he is in a given situation, the less good he's going to be about holding it. But he's gotten pretty used to car travel. In a car, if he's not in his flight suit, I offer to him at regular intervals to go to the bathroom (I bring a piece of newspaper and set it somewhere accessible). He has to always try, I use my thumb to try to make it difficult for him to just walk back to my shoulder

I potty trained him to go (if he can) when I hold him over something and say "go potty!"... though I've switched to "Viltu kúka?" and he still goes, so I think it's simply the action of holding him out over something and the tone of voice that cues him in)
Sometimes I travel with him in his flight suit. The downside to that is he'll chew at it and try to get it off. And while they're parrot-beak-resistant, they're not parrot-beak-proof.