It is ok to stay with him, what isn’t ok is to accept his apology and have nothing change.
He might be depressed, he might really have been struggling, but instead of taking the time to work on himself he strayed like a spineless worm. So now it is time for him to work on himself and become the man you deserve.
If he is depressed he needs medication and/or counselling. He needs to be truthful about what he has done, let you ask questions, let you be angry, let you feel everything you need to feel in order to heal.
You need to take the time away from him to get perspective. You need to work out whether you can forgive him and move on, and what boundaries you need to have in place, what behaviours you need to see from him to know he has changed. Then when you’ve done all of that, said all you need to, cried when you need to, you put on your big girl pants and make that decision…stay or separate.
You are enough on your own, and you can be a good mum without him, you don’t need to stay with him because you think it’s easier than separating. BUT you also aren’t weak if you choose to stay together, it’s not shameful, it is nothing you have done wrong, it is you making a difficult choice to try to rebuild.
Just as an aside, my husband (of 15+ years) lost his mum and then had a breakdown during COVID, he had an emotional affair with someone he worked with, fortunately they never actually met (thank goodness for WFH and distance) as for me I think physical contact would be a line I would really struggle with. But we are still together now, and happier than we have ever been, he had counselling and sorted himself out, we made changes to our relationship together, and he got a new job. It is the hardest thing I’ve ever had to go through, so if you do decide to stick with him be prepared for the tough road, but it has worked out for the best. There will be other people who have stories of leaving and spreading their wings and creating an even better life without their ex…there is no right or wrong answer, you can only do what is right for you.
Sending love, whatever you choose I’m sure it will be right for you 💐