ok, avhaben, didn’t get that. I think it says it clearly though, don’t need that proof.
Thye basic idea of listening to them is because of repect – point is not to disobey. R’ Moshe therefore says that maybe its only in front of them – i.e. as soon as you leave your mother’s house, you can take the coat off.
The questions about yeshiva is discussed in the poskim – def, don’t listen IF it’s clearly detrimental.