Hi OP - sorry to hear you're going through all of this awful stress. I can't try to give you any hope, but I can emphasise because I've been in a similar situation.
I discovered my husband had been cheating last summer when an anniversary card came to my house for him! Turned out the card was from an older mistress and he had a newer one on the go as well - real shocker because the man was so dull I'd never have believed it of him! He admitted cheating for two years with two different women, but I suspect there's more - but to be honest it really doesn't matter now, I don't care. Once was once too often and would have destroyed our marriage. The fact he effectively destroyed it many times over and made a fool of me for years just puts the tin lid on it.
There was no point in attempting any counselling or trying to work on the marriage because he had pissed all over it - it simply wasn't worth my time and emotional energy. I told him to move out, which he did without any fuss.
We had a DC12 and had been together 16 years or so. The thing is that there was never any hope for the marriage once I found out because it showed me how my husband was a complete stranger, also that he was a duplicitous, spineless weasel of a man, who lied as easily as drawing breath. I would never have been able to trust him again and I wouldn't have forgiven him.
Why on earth would I want to fight to try stay with such a man? For me? No, I'm worth far, far more. For DC? Certainly not - they wouldn't be happy living in a house with such a bad atmosphere and emotional upset.
What I want to say is that you are worth far, far more. Your baby deserves much better. You can't stay in a doomed, upsetting relationship for the sake of your baby - at least if you do split while the baby is young they won't even remember a time when you lived together and living separately will just always have been normal.
I don't think it matters how much counselling you have, how much you put yourself through the wringer of emotional turmoil and stress, the upshot is simply that you can't trust this man, he's proven that you cannot and should not trust him. You might be able to push it all to the back of your mind and try to ignore it, but it will always be there niggling away at you - which wouldn't be good for your mental health. And if in years to come it bites you on the arse - he does it again, which is likely - you'll be wishing you hadn't wasted your life on this man.
It's a rotten situation, I wouldn't wish it on anyone. But when people talk about "fighting for a marriage" and "making it work" I think, well, is it actually worth fighting for? Is it worth all the hard work and upset? It's your decision.
Just to say that less than a year later, my ex lives nearby and has DC alternate weekends, we're amicable, DC is happy and has adjusted well. I'm in a much better, happier place, with a newish boyfriend who has reminded me how easy, fun and mutually supportive a loving relationship should be. So please don't stay with your cheating husband because you're frightened of the future - wonderful things can and will happen for you, if you take control of your own future and don't allow yourself and your baby to be held as emotional hostages to your husband's extramarital whims and fancies.