Pee pee vs. coat

Today as we were heading up to Stars classroom in the elevator, Noah started doing the pee pee dance.
"Hold it!" I said, "Hold it until we get to the classroom don't pee pee in your pants."
I opened the door.
"Go! Go!" I said as Noah rushed through the door in delight. But then as I was signing in, he didn't go to the bathroom. Instead he was slowly taking off his coat. His coat was off and I continued to tell him to go to the bathroom but he was frozen there looking at me.
"Hurry up Shao you told me you had to go to the bathroom now go!" I realized later that the Pau Pau in the classroom was asking him to take off his sweatshirt first, by himself. I guess this is the classroom norm, the morning ritual, that every child must do. And Noah didn't dare disobey, even though his pee was probably trickling out into his underwear already. But all of this I thought later. What I thought at the moment was, "damn it!" I put down the clip board and rushed over realizing I would have to physically bring Noah to the bathroom again, otherwise I would have to change his underwear and pants, and I had a KUng Fu class at Little Panda's to go to, and I would have to just leave Jonah unsupervised.
After it was all over I could tell Pau Pau was mad that I had undermined her authority. Not only that, but the teacher had also said Noah should go to the bathroom. Maybe most kids don't pee their pants, but we are still having issue with this with Noah. The main problem is if anyone tries to make him go as a precaution, because there won't be time to go later, he doesn't want to do it. It is only at the last second when he really has to go that he will even allow you to go through the process of going to the bathroom. If that happens on the train or at the upstairs playground, basically there is nothing to be done because he is going to pee his pants. The other day he did this and I knew he was doing it because he went into the toy closet to do it. I questioned him, but he simply denied he was peeing. But of course later I found out that he had been.
Anyway, so i made pau pau mad, and after all, my son is going to be with pau pau for half the day (paus paus do a halfday and then are replaced by another afternoon pau pau) so if she decides to take revenge I am powerless. But what the hell the kid had to pee. You can pee with your coat on can't you? What's wrong with that other than that it is not how things are usually done?