A thought:
In the aftermath, post-fight discussion, your wife seems very quick to agree that you were right, that she was wrong, and it seems like you really believe her–you keep citing that as evidence that you WERE entirely in the right.
Is it possible that in the post-fight, she’s telling you what you want to hear? A lot of people do this: they just want the fight to go away. People raised by very authoritarian parents are especially prone to do this. They learn young that whatever the fight is about, however legitimate their grievances are, they will never win. They will be yelled at and berated until they submit, accept total responsibility, and come up with some plausible reason why they behaved that way. And in that moment, they believe everything they are saying, because totally, genuinely destroying their own ego was the only way out, for years.
With people like this, those post-fight conversations that seem so productive are actually useless, because it’s all bullshit designed to make the other person happy. They are just looking for what you want to hear. And then the issue doesn’t get better, because the real issue hasn’t been touched. The passive person doesn’t even know what the real issue is anymore because they’ve distorted their own memory in an attempt to find a version of the story that the other person will accept.
If your wife is like that–very non-confrontational–then what looked to you like “normal parenting” at the dinner table looked to her like a terrible fight, and she got upset because she wanted a happy family dinner. Then, when you talked to her afterwards, you were angry to the point of thinking about leaving her, and so it was urgent that she find a way to take on all the blame and all the pain to convince you to stay. But if this is the case, it won’t really get better, because you really do have a crucial communication problem–for whatever reason, she is telling you what you want to hear, and you are believing her uncritically.
Obviously, you aren’t the only once to blame and you both need to change, but what YOU can do is try to find ways to make sure she feels like she can tell you how she really feels, even if it’s not what you want to hear–that you aren’t going to argue back with her about how she shouldn’t feel that way, that she’s being unfair, that she’s over reacting, whatever. And when she does tell you stuff that makes you feel good and her look bad, think about it critically and ask questions.