I apologize, for myself, for my fWW, and for my kids.
I apologize for my fWW because she's trying to make amends. She recognizes the magnitude of her poor choice, and we're both working on making "us" stronger. While part of me may say she "deserves" to feel an echo of the pain I felt on D-Day, that's not at all useful for my goals.
I apologize for my kids because, as a parent, I need to model good behavior for them no matter how I may personally feel about a situation. When they surprise me with "kidney tag" and I curse, I apologize. When I snarl something vulgar at a driver who nearly t-bones me on the road, I apologize. And when I lose my temper at them or at my fWW, I apologize. I do this so that my kids will also do it. It's not enough to just tell kids how to be a good person, you also have to show them.
I apologize for me, because someone who's intentionally hurtful is not the kind of person I want to be. Whether or not I may feel that the hurt is justified, someone who intentionally causes others to feel pain just to make myself feel better is someone I reject. So when I fall into that trap, I force myself to apologize so that I can reinforce my own good behavior.
And that's why I'll often suggest to people here that they apologize for their own hurtful words or deeds, even if they feel those actions were fully justified. We become who we practice being. If we let ourselves act, consequence free, on our angry urges, then it becomes easier and easier to do so in the future. If, instead, we rein in those urges, if we practice being kind and gentle where possible then that will become easier. I should note, also, that "kind and gentle" doesn't mean "weak and easily pushed around." I am kind and gentle, where possible, because I am strong enough to be so.
Hopefully that makes sense.