I don't think there is much value in doing anything until you have a clear idea of what comes next, for you.
Is this the end? If you don't want to split, is an open marriage on the cards? Do you want to just forget you've found out, and carry on as you are?
For me, that'd be it. It sounds like the marriage was over anyway, and he's been lying to you for years. He's not even putting much effort in, just placating you by telling you he loves you and then falling back into old habits and routines. I'd ask him to leave and take the headspace. Speak to him in a few days, if you want too, and either talk about this or make plans for who will live where, contact, etc.
There will be devastation, if you split, that's probably unavoidable. There is devastation now, though. Whatever happens now, you have his mess to clear up. Your children will be okay, whatever happens - it's probably preferable to them that they don't grow up in a loveless marriage, where he shows you no respect, because they will model their relationships on yours. But regardless of if you stay or go, you'll be okay, and so will they.
It's probably wise to arrange STI testing, too, if he's been on dating sites for years. Just in the sense that it's better to be safe than sorry.
I am sorry that he's done this to you.