Ignore the negative posters and try not to let them get to you. Some people on MN seem to struggle with empathy and genuinely seem to think that insulting someone is the best way to make them see things from their point of view.
You have been put in an absolutely horrible position. Of course, ideally, it would probably be easier for him to be out of the home while you process everything. But from the reasons you’ve given, that doesn’t sound realistically possible without making your life harder or potentially affecting your daughter. Why should you have to suddenly solo parent or have your child upset when you are completely innocent in this situation?
I would suggest putting a routine in place where you split the childcare responsibilities and have a clear schedule. Stop cooking for him, doing his washing, etc. You don’t need to make a big deal of it or make the change obvious to your child at this stage. It can simply be “Daddy time” and “Mummy time”.
The purpose isn’t to punish him. It’s about giving yourself some autonomy and independence and, importantly, giving yourself confidence that you can manage on your own. If you ultimately decide to give the relationship another chance, you need to know that decision is coming from a place of strength rather than fear of change or being alone.
I would also tell him that making it up to you through household chores or doing all the “right” things isn’t as important as being brutally honest with you. It’s not uncommon for someone who has cheated to desperately beg for another chance and say and do everything they think they should. But ultimately, once the dust settles, whatever led them to cheat in the first place is still there.
You don’t need his apologies or to watch him suffer. You need the truth.
He acted the way he did for a reason. Was it because he is struggling with his life as a husband and father and craving the excitement or freedom of his younger years? Or did he develop a genuine emotional connection with this other woman that made the risk of losing his family and the life he had worth taking? Does the thought of being on his own, or potentially being with this OW, fill him with dread or relief?
Those are the things he needs to go away and genuinely reflect on. Not just the immediate, autopilot panic of his life changing and the instinct to say or do whatever is necessary to stop himself losing control of the situation.
Rebuilding trust, and potentially love, could take years, if it is even possible. So before you consider trying again, I think there needs to be a really honest and practical conversation about all of this. Perhaps with the help of a counsellor, so that you can both get beyond the immediate emotion and actually understand what happened and why.
Good luck ❤️ You are strong, and whatever happens, you and your DC will be okay. Stay true to yourself.