Sorry, no. There is a peculiarly unique American phrase: "never complain, never explain." I'M APOLOGIZING TO NO ONE, PERIOD. Let alone the nasty poster you refer to. I would rather have my tounge dragged across a parking lot full of broken glass.
So let's get back to it then...I'm up for it. FOR HOURS & DAYS. Please, by all means--GO RIGHT AHEAD.
It's all part of growing up to realise that one should apologise when one is wrong - it's a pity that you haven't reached a level of maturity yet that you understand that being gracious is far better than indulging some juvenile idea of machismo.
You should apologise to her even if you don't like her, because what you said is out of bounds in how a lady should be treated.
And the threat of hours and days doesn't phase me in the slightest.
Ivan