AITAH for telling my daughter to give us another chance or to have a strictly cordial relationship?

Hello, all. I'm a father of four, three girls and one boy, and I have a very complicated relationship with my youngest daughter, Maddie. To summarize the best I am able: her mother and I have been through a lot while she was growing up. Her mother has bipolar depression, and from when Maddie was about 5-11 either was not properly medicated or did not take her meds. As a side note, I have autism, and I have just now recently come to accept this fact. It has truly limited by ability to communicate. I traveled for work on the weekdays, so I was not home to help care for my four kids. This, unfortunately, resulted in a lot of traumatic events that I wish did not occur. Her mental health made our relationship extremely strained, and Maddie was exposed to a lot of arguments and bitter fights between us. I do admit that we fought more than was healthy, and she saw a few times talks of divorce. We moved twice before Maddie was fifteen as a result of my wife's mental outbursts. The huge even though was when I found out my wife emotionally cheated on me with a co-worker. I was so angry, and I admit that I took it out upon my daughters and son for the next four years. I do think though that this was a better solution than the alternative, leaving them. In short, these tensions produced a lot of bad environments for Maddie and her siblings, resulting in bitterness and anger.

The issue becomes is now that Maddie is twenty, and she has grown extremely angry about her upbringing. She is home for the summer, and she treats us horribly most of the time we are around her. It's quite honestly like we are walking on egg shells with her. She constantly brings up traumatic events she went through while my wife was mentally ill, such as my wife threatening suicide or the trauma she suffered from my yelling throughout the years. I am not saying she cannot bring this up, but my wife and I have undergone three years of therapy to fix our relationship, and we have moved so far past her childhood and teen years. This all came to a head three days ago, when Maddie told us that she did not feel like we listened to her. She was psychoanalyzing the way I replied to certain things, as if she was justifying why she felt unseen. I told her that she just missed her college friends and that we aren't a substitute for it. She denied it, and she started to speak about the last year and how she felt unseen. I was honestly fed up, because we have been trying out best to form a new relationship with her after her childhood, and I told her it was bullshit. This lead to a huge fight where Maddie claimed that we abused her her entire life through verbal abuse and also being exposed to my wife's mental health. She claims that I was not healthy and treated them poorly, despite the fact that she was better off than 90% of kids financially. I understand where she is coming from, and I apologized to her for it, but I told her that I will not beg for her forgiveness. I admitted to some of the verbal abuse, but I refuse to sit there and say she was abused for her entire life. She got really upset at this, and began to yell and cry. I told her that she was not recognizing that she also made mistakes when she was growing up, and she yelled that even if she did, she was a minor and was not responsible as I was the parent. At this point, I asked her to do family therapy and she refused on the basis that when she was a kid my wife turned her private therapy sessions into family therapy (she would talk to her therapist about her behavior and try to fix their relationship. It was meant to be helpful, but Maddie didn't see it that way) and then "stole" her therapist when she was 11 as my wife "begged" Maddie to see the same therapist as her, despite her initial refusal. I was done with her targeting my wife, who at the time was extremely mentally unwell, so I told her that she could take her ire out on me, not my wife. I don't think my wife is to blame, and I told her that it was like blaming her trauma on something that happened in childhood. Eventually she has to grow up and face the facts of an adult relationship.

She told me that she was unable to move on from what she suffered, and then began to list even more events of hers, such as times that I yelled at her or my wife did. She cited the lack of support and criticism in her current major as a reason of abuse. I responded that while, yes, I was not supportive of her decision and I was very critical, for the last two years we have supported her. I told her, again, we could do therapy, which she refused. I was done playing this game, and I told her that either she can give us a chance or we can have a strictly cordial relationship because there was no were else to go. She can't keep treating us like her punching bags. She told me that she doesn't know what else to do, because if I couldn't admit she was abused her whole life (not just only a few moments), she can't move on. I told her I wouldn't lie or beg to her. Maddie then told us that we can keep a specifically neutral relationship moving on, and then she told my wife she wouldn't be going to a planned movie with her tomorrow due to this. My wife broke down, and I was so angry at Maddie. I asked why she would do that, but Maddie responded that she was doing what I asked her to do, but this wasn't what I wanted. She asked her mother if she was hurting her, and I told her that she was. She looked shocked, but left. I tried to console my wife, but it took a good thirty minutes.

I'm at a loss on what to do now. We saw each other today, but we didn't say a word to each other. She claims she wants a relationship but either can't right now or not under these conditions. I'm sorry to say, but I'm far past justifying her behavior towards my wife, who was mentally-ill, and myself who suffered from anger and autism that I couldn't control. I truly tried to explain to her regarding the latter point, but she said that it wasn't a justification for the way I treated her. I do admit there was some verbal issues, but honestly, that's just parenting. I apologized to her, and I can't change the past.

AITAH?

TLDR: My daughter Maddie claims that she was verbally abused her entire life because my wife was mentally unstable and I suffered from anger due to her emotional cheating. She claims that we can't have a relationship until I tell her she was verbally abused, but I told her I wouldn't beg. I ended up telling her that she can either give us another chance or take a step back.