I'm wondering how a sister who doesn't even live nearby her can be that big a source of stress to her. I mean, like what is she doing for her sister?

It seems pretty clear that your mother is not wanting any reconciliation. She just wants to paint you as bad as possible. If I were you, I think I would stop expecting anything from her. Groveling before her clearly did absolutely no good at all, and she just respects you even less for that. So make up your mind that you are not going to do that anymore. It just feeds into her delusion that you are guilty of something terrible. Hold your head up and never put yourself down again to try and placate her.

Say to yourself, "I'm a decent person and I have nothing to hang my head in shame about. I'm available to connect with my mother in positive ways, but I will never again participate in this false narrative that I need her to forgive me for being horrible to her."

I have a very disturbed brother who goes around entertaining fantasies about how everyone has wronged him. I used to go so far as to write him letters of apology for times when he became offended because some conversation he had with me didn't go his way. I bought into the idea that he needed validation, and I tried so hard to give it to him, putting myself down even. He became so much like how you are describing your mother that it is uncanny.

This is a fantasy world these people are living in and their delusions border on and even cross over into the realm of psychosis. It's tempting to think that they are just wounded souls who need an abundance of kindness and love and acceptance to be able to overcome their psychic wounds. Thinking about what you have shared has actually helped me to understand better what I went through with my brother.

They have told themselves lies and they are capable of great cruelty. Nothing they ever do is wrong. Everyone around them is always guilty of mistreating them. (Are you the only person whom your mother is this blaming of, or is she always finding fault with others and never with herself?) Believe me, I tried the kindly approach, and it went about as successfully as your recent conversation with your mom.

Looking back now, I realize I was just enabling my brother's pathology, by bending over backwards to show him tolerance. If I am ever in his presence again, I will have zero tolerance for listening to his absurd claims to having been victimized by me and others. Stand by your truth, as I should have done. You have not wronged your mother. Stand by that. Refuse to buy into to this alternative reality that she has created that has little to do with the truth. She is uninterested in truth. And don't help her make mountains out of molehills, by going around in sackcloth and ashes hoping to atone for some triviality of the past that she is recasting as THE GREAT OFFENCE, from which she can never recover.

You may have to accept that your mother really doesn't want a reconciliation. Visit your parents, if you wish, and act pleasant, but stop trying to placate her. If she starts castigating you for some terrible offense, say "Mother, that kind of talk is a bunch of nonsense, which has nothing to do with any of us today, and I just won't listen to it."

In her head, it's like the needle got stuck on the record and replays over and over. You'll do her more good by insisting on not getting stuck, as she us, playing the same fragment of a tune incessantly. Change the subject and move on, with her, or without her.