You will never ever be able to move forward from this.
Often when someone cheats it might be at the Christmas party or on a business trip abroad, or on a lads night out. If the partner finds out and tries to move and they are often still triggered massively at the next Christmas party or lads night out or when they're away on business.
In your case he tried to cheat in a place where he would easily be caught. You would never trust him even if he was in the company of your friends, if your children was there. If you were there. You will always feel paranoid and anxious about this. It will absolutely play havoc with your mental health long term. I can't see a way to move forward from it.
I can understand you're scared of leaving him, he's all you've known for your whole adult life. You're right, it does make it worse. You don't know life without him. I left my ex after 12 years and had been with him since I was a teenager. I knew I didn't want to be in the relationship, but it is so so strange and difficult when they're all you've known for your adult life, but there are lots of people in the same situation and who have left, it does get easier and then eventually people are glad to have ended it.
You say you're worried about destroying the kids lives and mention activities and stuff, tbh their life will have already changed, if you stay now and keep up their activities etc. they are still technically in a broken home, relationships don't recover from this. It is far far better to start to carve out a new life for yourself. At 3 and 6 it is easier to cut activities if you need to for now, rather than if they were older kids. Your kids will adapt.
I haven't seen the post where he hit you, but obviously that is another serious issue, and you can't live in that environment.
I'm so sorry you're going through this but you will be able to make a new life for yourself.