@Namechange20002 You may need space to calm yourself down, but don’t make any rash decisions like unilaterally ending the marriage or kicking him out without a proper, honest conversation. Right now, you need to set aside your anger for a moment, talk to him openly and honestly, and listen to him. And he needs to afford you the same courtesy. Don’t put it off, don’t let it fester - you could do more damage overthinking, building more anger, withdrawing further, than opening a dialogue and beginning to address the issues.
Don’t wait for him to come to you either—if you both retreat into silence, you could end up in a Mexican standoff, and before you know it, your marriage is unraveling, you’ve separated and you can’t get back to your precious family unit.
I imagine he’s feeling embarrassed, ashamed, and likely caught off guard by your visceral anger. He clearly knows he’s done wrong and has retrenched.
Marriage and family life are hard work at the best of times, but it sounds like you’ve both been struggling physically too.If your life together has been mostly happy, and he’s generally been trustworthy, start from there; not the assumption that he was trying to start an affair, that he’s a misogynistic prick, and that he was trying to manipulate your child, if that all seems out of character. What matters is how he owns his mistakes and what actions he takes to rebuild trust.
Personally, I’d be really embarrassed by what he’s said, and I’d be calling into question his judgement. But I’d also be listening to what he’s actually saying to her - he’s clearly unhappy, perhaps more so than he’s letting on to you and that would be a focus of conversation for me. Why hasn’t he shared this with you? Why does he feel comfortable sharing this with her? You say you’re very private - is the same? Is he someone who needs an outlet and has chosen the wrong person and gone about it in the wrong way? What’s your instinct saying?
No one can tell you what to do, but I hope you can at least talk and listen to each other. If deep down you still see a future together, then it’s worth fighting for.