I think it is often a harder road to travel to stay and try to forgive, but there comes a point where you have to analyse whether it's worth it to you in terms of the person you've become - and especially, your own self-respect.
This is where staying to give the children stability becomes a bit of a red herring. You need to work out how much of your decision is about them, how much of it is connected to your own fears of going it alone and how much is bound up with loving him and believing him to be capable of change.
Likewise, he should be going through the same process. People often stay together after a crisis like this, on both sides, for all the wrong reasons.
You're suggesting giving it a year OP, but you are already 9 months on. During that time, your H has done precisely nothing to analyse his own behaviour and take steps to ensure it never happens again. Instead, he feels the matter is closed and resists talking about it again. He won't go to counselling, won't look for a more marriage-friendly job and won't talk about his feelings.
You seem to be hoping for a cure for feeling the way you do, when actually what you're feeling is natural and is your Psyche's way of telling you that you need to do something different. Have a really good think about what you need from him and dare to ask yourself whether this man is good enough for you.
If you accept so little and still stay, then go into that decision with your eyes open. Think about the effect it will have on your self-respect and your other relationships. Think about how that could change your way of looking at the world, so that you end up feeling as though you are now a different person - and not in a good way.
If you can't get him to counselling, then go yourself. You would really benefit from a skilled professional helping you to unpick the choices you are making - and the reasons you believe you have for that.