Hey Horrorfan2021, I'm also a fan of Horror, the pulpy 1920s kind from Robert Howard, Clark Ashton Smith and Lovecraft, as well as Asian and Scandinavian horror movies. You should post in the Book Club some time.
However.. the matter at hand. It seems to me that you have at least some definitive proof that your fiance cheated. You have her admitting she did what she did and has the feelings she has. You have clear evidence that she is with her AP now and in a relationship with him, not you. So.. I'm wondering what you want advice about, actually?
You're not in the awful discovery phase, which is a relief. You know what you know and you have it confirmed. You took what I suspect is appropriate action. Don't torture yourself with any doubts. Reading this bit:
A couple of weeks ago we had a birthday party for our son, at the party she asked why I'm being "so cold" with her. Acting like I should be her best friend after she'd broke my heart. At the party so also told me she still didn't know if she'd made the right decision. She also said "we" alot. "Do we have this? Do we have that?" As if we were still a couple.
I sense a man who might be doubting his decisions. Don't be fooled by this routine. You've been doing some research, I can see you know what the 180 is. She is reacting to the negative stimulus of the 180, which WILL cause a reaction, albeit not always a good one. You want to know why she is saying "we" constantly? You're parents together, for one thing. You are going to be making decisions together, in a non-married state, for a long long time. Get used to this.
She might be talking like this for an audience-- possibly just you or possibly other people (to show she's not the bad guy here). She MIGHT want them to think that you two are totally okay with each other after the break up and one of these cool, elevated type couples that can work together for the good of the child, be the best of friends and accept their ex-spouse's new partners objectively. You know the only part of that that's true? The "Work together for the good of the child" part.
You don't owe her friendship. Friends don't behave like this (at least not my friends).
Friends don't betray each other and hurt each other. I don't like people like that and I certainly don't stay friends with them. I suspect you don't want to, either.
Here's what you owe your ex-fiance, the sum total of all of it: Cordial cooperation for the common good of the child you had together. That's incredibly important. You won't have the option of blowing her off entirely. that happened the day your child was born. You could, if you find communication with her difficult, resort to email and coparenting apps. That will minimize contact to the bare minimum.
You owe your child your love, affection, and support (financial and otherwise) for a long time. You owe your CHILD that, not her. You just have to deal with her because she's the other part of that deal.
Lots of people become, over time, great co-parents. Even people who loathe each other have the capacity to put it aside for the child's sake. Don't fall for any manipulative tactics like "I'm so confused", "It was a mistake" or "I don't know what I want". In almost every case, they aren't confused at all, they made a decision (not a mistake) and they know what they want. Really, really. So don't get any false hope going or think she has reignited the flame because of her being manipulative. She knew exactly what she wanted when she introduced her AP to your child. Don't forget it.
BTW, if you don't want the AP around your child, you have parental rights in this situation, you know. What does your lawyer say?