I'm so sorry. And your poor children, living with the knowledge he was cheating and then having to tell you.
It's just wrong; of course I'd want to know how far it went, but everything you know so far is enough to leave him over.
4 things to do now, to give yourself time to think:
1. Withdraw and move at least half the joint money into accounts that you control.
2. See a lawyer now,before he does. Knowledge is power.
3. Individual counseling for you. This will help you make decisions and regain control (No joint counseling until you are stronger and know what you want to do.)
4. Remember your kids are watching you to see how you handle his infidelity. What he's done will affect their future relationships. If it was your daughter being cheated on, what would you tell her? Would you really tell her he says it's not physical, so o try to work it out?
Of course not. You love her. You'd want to protect her and help her leave a relationship with a cheater.
Love yourself just as much. Your children have tried so hard to protect you. Protect yourself and them now. Demonstrate strength and self-respect. Be pro-active and show them you won't put up with his behavior, that no one should have to put up with that. You may not feel strong at all, so fake it until you make it. You will get stronger.
I know this, because like your daughter, I watched it happen to my mother. She showed me that you can make yourself stronger; that no one treats you that way and gets away with it. She wasn't always fierce, but she used her anger and learned to be.
Wishing you find that strength too! ❤️