Owning your shit and apologizing genuinely (hint: this does not involve an I'm sorry but/I'm sorry you feel that way/I'm sorry that my attempt to be awesome just wasn't what you wanted/I'm sorry I'm such a horrible catastrophe who need to go eat worms) as well as, shutting the fuck up when you're asked to do so at the time goes a long way to settle/rebuild relationships.
Though depending upon the offense and what happened it doesn't always salvage your participation.
I think it's fine to disagree or whatever, but honestly it sounds like you just did not listen when told to stop. Stop means stop. If you cannot it's best to walk. For the night/week/permanently/whatever.
Yes, even if you thought you were tirelessly working to improve your family/group/the game/whatever. It's not fair sometimes, and some folks are better than others at recovery. I think a lot of us mushers have difficulties with knowing when to back off or change tone, ect. But when you are given explicit direction, just...I don't know. If you truly want to stay on a play just bite your tongue and do it, and give it some time to see if you still want to play, with that restriction, once you're not in the moment.
And there is never, ever a good reason to go off on a channel, especially a public one, ever. Even if it's about game stuff like systems and stats. Just don't do that unless you're on the Rules Lawyer channel with other people who love that stuff (there's always a few, keep it to there so you have fun without stressing everyone else out.)
But really. Sometimes even when your dander is up and you're about to saddle up that tall horse, especially if it's with staff on their game--it's wiser to just shut up.