Ok, deep breath.
He’s a bastard. You know that. You are (rightly) focussing on taking your children’s pain away.
Here’s the benefit of hindsight as someone who was in your children’s position when I was a similar age. I’m sure a lot of this has occurred to you anyway.
My dad introduced me to the affair partner whilst it was still an affair, before he left. I sat in the front room with her very embarrassed grandfather whilst they were otherwise occupied.
Then, soon after, he left. And I was destroyed. Absolutely heartbroken, confused, shattered.
It’s good (well, better than it might be) that your children are crying, that they are obviously distressed, that they are additional support. It’s better that than they bottle it up, stuff it down, leave it to fester for decades.
You can’t control his behaviour. As you say, he’s got no better nature to appeal to. He is utterly selfish.
Let your children talk about it, cry, talk about how they feel. Let them grieve openly (because it wasn’t til after my mum died many years later that I realised that what I had experienced as a child was grief).
He may or may not stick around in their lives. If he does stick around he may foist all manner of relationships and arrangements on them. It will be hard for them and they will get distressed.
Don’t ever let them think they have to hide their distress from you. It is so, so shit that they have to go through this, and that you have to support them through it. They will be angry, sad, confused, distressed. Let them have their own valid emotions and responses and work through those. Let them grieve in public. It will be quicker, easier and better.
Never think for a moment that any of this is your fault. Never for a moment let them think it is any of their fault.