Please understand that I am neither pro-R nor pro-D. My only hope for any betrayed spouse is to find their own way out of infidelity, to find their own path towards peace of mind, body and soul. It is only when we can find peace with ourselves that we can find peace with the rest of the world.
It's seems that your WW has set the terms and conditions of reconciliation and staying married. These terms and conditions are unacceptable to you, correct?
In every relationship we have (family, spouses, friends, coworkers and bosses) we automatically, instinctively, establish a relationship dynamic. These dynamics govern how we interact with these people. Your WW is well aware of the dynamic she's established with you and knows exactly which "buttons" to push in order to manipulate the conversation and, by consequence, manipulate you.
You, sir, have the power to change this dynamic. It begins with establishing boundaries.
Infidelity is not a mistake; it's a choice (a series of choices, actually). The next time she insists otherwise, you have a choice to make. You can either accept this untruth and let it go at that, or you can choose to not accept it and let her know, in no uncertain terms, that you refuse to live with it.
I have long advised betrayed spouses to get as comfortable as possible with both reconciliation and divorce. It's something that was drilled into my head when I was a new member many years ago. Without allowing yourself that choice, that freedom, you surrender control over your own happiness and well-being.
I would imagine that your wife has zero interest in doing the work that R requires; owning and fixing her shit. She will not admit that infidelity is a choice because that would force her to accept that she is capable of such base and self-destructive behavior. And that's exactly what infidelity is; self-destruction. So, she keeps insisting that it was just a mistake, which negates her accountability. Everyone makes mistakes, right? It's bullshit and she knows it, but she can maintain this nonsense because she knows you'll do nothing to change this dynamic.
Now, it's up to you to decide whether or not you're willing to live with this crap. I understand from your previous posts that family is everything to you and that separating or divorcing is off the table. If that's the case then you're living in a prison cell of your own creation and have no one to blame for that but yourself.
It's high time for you to establish your own terms and conditions. If you truly want to save your marriage you're going to have to risk its demise.