What do you actually want in an ideal world? To have no contact with him? For him to be a father to your child? For you to end up together in a fantasy of hearts and flowers? For him to be faithful to you?
I think you need to be really REALL honest with yourself here because it will inform your actions.
If you actually deep down want to keep being the OW or have a real desire to become the primary partner (for this guy who is likely to still be unfaithful) you may come to realise that anything you say to him has ulterior motives. (the subconcious hope that the ultimatum will bring him running).
If you really want to break it off but are open to him being involved in his child's life, then I would meet him (you are a grown up after all and about to become a mother so you can be civilised and well mannered even if he is a cnt) and tell him neutrally and calmly that you know about (what you posted about), that any relationship between you is over, you don't appreciate him trying to blackmail you by bargaining access to him with your child's life and you are deeply disappointed in him for that as you thought better of him (although you may want to leave that bit out). However, he is as free to be involved or not involved in your child's life as he wishes; that you won't block access but beyond contact related to the child you aren't interested in anything beyond an operating civil cordiality for the sake of your child.
The ideal place for this meeting would be somewhere neutral that is quasi private - ie. not your place or his but a public place where you can talk without being overheard.
[*in my experience, telling people calmly you are disappointed in them and expected more of them, really freaks people out and gives you a massive upper hand in a stressful and emotional situation. I think it's something to do with the fact it's the kind of phrasing that parents/teacher used as a child and it has a deep psychological resonance in an emotional situation.]
Sorry you are in such a terrible position and hope your future holds lots of lovely things.