It is not really owning it with actions if it is littered with appositive phrases and "buts." There is no "spin" to be had here. She cheated and hurt her family. Things are never going to be the same.
I think that you are just not emotionally capable of understanding that I didn’t do this to cheat
Veiled dig at you aside, intent really doesn't matter to you does it? She cheated. She spoke ill of you behind your back. So she did not actually betray you and her marriage ? I am confused (sarcasm). She did cheat. That fact has been established. The rest are details that don't change the facts.
I just think if we were to talk about this together to people, you wouldn’t see this one- sided response.
How is this not justifying her choice to cheat again, exactly ? What is one sided? That she made a choice, without your involvement and now expects you to accept responsibility for that choice as if you were involved in that decision? Facts don't require an explanation and they aren't up for debate. Manipulation attempt again.
Figuring out why this happened and learning tools and coping mechanisms is what will heal us.
This did not "happen," she put energy and effort into making it happen. Why did she do that is the real question.
Why does she talk about, you this and you that, but suddenly it becomes about healing "us." She is trying to give the impression this is an "us" problem . It is a "her" problem. You were in the same M, but did not cheat. She can't stand that fact either.
He’s trying to fix me separately and in turn, fix our marriage if that’s what we want
She has to fix her. He is a resource to aid her. Only she can "fix," her. The outcome of the M is independent of if she can "fix," herself. BTW the M being reconciled is not a "given." You do, and should, have doubts about taking another risk with her. What is she willing to do to make you feel safe ? Actions, not manipulative words, are the only way to gauge her sincerity.
if that’s what we want
It is about what you want now. She made her choice already. If she was so unhappy with the M and her life why did she not seek help and/or end the M ? Hint: She was fine. Remember cognitive dissonance. Somehow she still wants to be the "good" person in all this. She can be again, one day, but right now she has not lived up to the integrity and character standards that she expects from others. She has no authority on character, integrity or authentic living.
I am trying not to sound too harsh to your wife, but I see a lot of words and not a lot of actions. She isn't even close to remorse. It is mostly about how it impacts her. As are borne out of selfishness to a degree where even the people they profess to love and care for aren't a factor. Her temporary indifference to you allowed her to cross those boundaries when she wanted to.
She can put all the psychobabble she wants into texts, but she choose to believe a bunch of lines from a player and idealize there to be a future there (Millionaire, right?). Now she is retreating trying to minimize the damage so she does not end up with less than she had before. She believes she can manipulate you back. She is deeply afraid of losing everything. She gambled and she lost. Now there is no one willing to fight for her and fall victim to her manipulations.
Anger/Rage are secondary emotions and one of the few that most men feel comfortable putting forward. I would tell her that and explain there is a mountain of pain, grief, fear, etc. Even her counselor would likely have to agree with that.
What has she really done, apart from finding an IC that tells her what she wants to hear, to help you feel safe ? Has provided a NC letter? A timeline? Offered to be 100% accountable for her time. Allowed you access to all her devices and accounts ?
These things are important. Any resistance on those things indicates she really isn't up to the task of repairing a M that she broke. Anything previous to this were dents that could be hammered out. Her A broke it to the point that a new one will have to be rebuilt.
Keep reading and posting.