Tell your GF something along these lines:
You are free to be with OM and whatever. I place no obligation or have any expectation of you. I am moving on. I will strive to be the best coparent I can for the sake of our child, but I need some emotional distance from you while we establish a non-romantic relationship moving forwards.
Then leave.
Get everything in order.
Is there a formal custody arrangement? Is it clear how support and benefits go?
Do you have any joint asset or debt or commitment?
Clarify everything. Start the process of separating your lives.
You don’t have to hate her, but as a rule people that separate don’t hang around being friends. It’s OK if you can, and possibly in a year or two it makes sense. But for NOW distance yourself. Detach. Recover emotionally.
Thank you for a clarifying post, helped sort my head out a bit. Thank all of you above, actually, good advice and I greatly appreciate it! I agree with most of what you write, with the exception of her being with the OM. I mean, I completely understand she being free to see whoever she wants, but I’ve told her that I never, ever wanna she that man around my kid - I’m not sure how I would react if he was to be around my kid. Don’t think he is long term though, so hoping I’ll never have to face the issue.
I’ve also told her I want absolutely nothing to do with her, I want her GONE from my life,with the only exception being necessary custody related communication. It’s gonna be quite a change for our son, as he is used to us being a close knit family. Breaks my heart. But the alternative is me being completely miserable with her being (seemingly) happy when all three of us are together, and I don’t want my son to see me that way. She’s really good at pretending, obviously (or maybe she just cares/cared so little for me that she isn’t heartbroken in the same way around me).
The formalities are in place, though she owes me some money I’ll probably never get back.