Both of these situations are something I would have dreamed about doing several months ago and in both situations, the issue was diffused the moment accountability was taken onboard. I look back on r/s with exBPDgf and there were so many times like that I should have spoken up but never did, instead choosing to take responsibility myself for the actions and behaviours of others. I'm glad I have the opportunity to see these things now and in the same respect passing this down to my daughters too. On the other side too, also trying to teach them that when the responsibility lies with you, taking ownership and apologising is the right way to act, that it's a 2 way street and that being sincere is better for all involved.
It warms my heart to know you are breaking this cycle, for yourself but especially for your daughters. In the kind of conflict situations you talk about, when an adult was angry at me about my (actual or supposed) actions, my mother forced me to say what the person wanted to hear (apologize, express gratitude, whatever) and get out of there asap. She says that she was teaching me to protect myself, but at the time there was no empathy talk with her afterwards, let alone during, where she considered my intentions and rights.
So it takes self-awareness and courage to do what you're doing, and I'm glad.