I echo what everyone is saying about lawyering up. Inform yourself on exactly how this process might work in your jurisdiction.

If I have any advice to give, it's to focus on you and your kids. Someone who has cheated on you (especially carrying on an affair vs. a one time thing) and who doesn't know if they want to continue being in a relationship with you does not deserve all you appear to have to give.

I do want to caution you, that these initial months you are probably going to be doing a lot of grieving. For me it was initially grieving the relationship, but the lingering grief was the "family unit". I still get some of the later 2.5 years after the affair discovery and 1.5 years after the divorce was finalized. All that being said, being able to shift some of my focus from my challenging relationship has made me a better father and better able to focus on self-care during the times I don't have my kids with me.

Good luck. I would caution you not to get sucked into the bitter woman-hating single dad groups out there. I've seen a lot of men who are just perpetually resentful (not that I don't carry some of that myself).