Sex addiction, my arse 
He just wanted to. End of.
Why his talk of not seeing his kids grow up, and your talk of destroying their lives?
My XH used prostitutes. We'd been together 8 years, married for 5 when I found out - and it was all this time. Well, I say found out - I had suspicions, that was when I found yet more circumstantial evidence and finally came to the conclusion that "just looking" was enough of a reason to divorce him. (got the evidence later, and of course he was) Anyway...
I didn't destroy my child's life!
She's a little bundle of happiness who loves both her parents, does about 30% of her time with him, thinks the sun shine out of his arse, and actually spends more time with him now that she did before (because he can't shirk it)
She thinks that we didn't have enough in common to make stay together. Which is true - I respect women, I respect myself, I respected my marriage vows. All things I didn't have in common with him 
You're in shock. Be kind to yourself. Tell him to get his second hand (third hand, 200th hand) filthy dick away from you. Take some space. Talk to a solicitor.
And don't forget that taking the serial cheating and risking your health out of the equation, you've said enough other things that make me think you're better off out of it.
There are plenty of happy children from divorced families seeing both parents regularly, there really are. 