It isn't really an affair with that level of distance and time living away. It's much more likely a full blown relationship.
As painful as it is, he seems very checked out. Not coming back when your child has sepsis is a massive disconnect from his family and children.
He has a whole separate life that has been built up for more than a decade.
If he wanted to be married to you and an active and involved father to his children, he would come back. End the affair.
But that isn't the life he wants. He wants the fun, freedom and being able to pat him self on the back pretending he is doing his part by financially providing for you all.
You have been doing it all for so long. But that was thinking you would have your time at the end of this period to experience the things you wanted.
You clearly are a strong person, you have been in a half way house for so long you probably don't even recognise how capable you are, because you felt you had a safety net in him.
The hospital incident along should show you, you haven't had that.
I would get very very clear on the financial aspect of things as a priority. Then think about the time, space and social circle you have currently.
Personally I would be so angry with him I would need to be in front of a therapist ASAP so I could express it without blowing everything up until I really understood what my financial future would look like.