Im so sorry - this is an enormous revelation and a huge shock for you and you must be absolutely reeling. Here’s what I would ask myself, when I felt able to (and appreciating that this might not be straight away)…
This man has two daughters (presumably different mothers). His younger daughter, who is now 10, has lost her mother, whom presumably she lived with full time, in the past year. This young girl’s mother has died. Regardless of how much or little contact he has had with her up until that point, he knew that she has suffered this loss. He did not: IMMEDIATELY make HER needs the centre of his universe. He did not instantly come clean, explain whatever complex backstory has created this situation, made it clear to HER that she has a father who loves her, a sister she can have a relationship with and (if this is something you had been able to work through together in the light of such a revelation) a step mother, step siblings etc etc who would offer her love and support.
I find it devastating to even imagine what that poor child must be feeling and very much hope her guardians are close family/friends on her mothers’ side and that she feels very safe and secure with them.
He has shown you who he is and it isn’t pretty. At best he is a disgracefully selfish coward.
However, I think I would want all the information on the backstory. AND I would want to know exactly what this child’s situation is now before I could begin to make any decision as to what to do next. Clearly there no long term future in being with a man like that. But I don’t know how you feel about his 17 year old, how old your children are, whether this child is vulnerable or in care etc etc.
Essentially I suppose what I am saying is, if I felt that me kicking this guy out or otherwise ending contact with him, would result in two devastated children being left at his mercy with no mother figures to turn to, I’m not sure I could do it. If the youngest is in a very safe situation and the eldest is nearly done with school then I would probably be tempted to try and manage the situation through the initial revelation/crisis and remain a point of security for all the kids until the eldest had finished A Levels and then cut ties with him (retaining a relationship with his eldest adult daughter, if it’s what you both want).
This doesn’t necessarily mean he has to live with you full time in the short term. And all of the above thoughts may be entirely wrong for your personal situation, of course.
The way he has treated you is appallingly dishonest. Whatever you feel you must allow yourself to feel - none of this is on you.
But if his eldest daughter is in the dark too, then the same goes for his treatment of her. She will also be feeling all this shock and need someone to lean on and share this betrayal with. And his poor younger daughter.
My heart just goes out to those children, and of course to you. I’m so sorry 💐