I would suggest he leaves. If he was my SO

His daughter is being used as a massive smoke screen (a beautiful innocent one at that) to hide what he really wants,(her mother) but he's not even hiding it well at all.

He wants to be with her mother, but claims he wants to be there for her.

If this was really driving him to the depths of despair, logic dictates that he would do his best to bot let history repeat itself, and thus be a better father to his youngest.

He says his ex robbed their daughter of a proper family, he's doing the exact same thing to your daughter, he's not pulling his parental weight with the daughter he does live with... Hypocrisy much?

Does the daughter the two of you share not count? Does she not need both her parents?

Or is she being left by the wayside because he can't play happy families with his first born, so now baby sister suffers as a result and gets robbed of the experience he's hell-bent on sharing with his eldest?

There's zero logic behind his dramatic lamentations, when you stack them up next to his actions.

That little girl is a smoke screen, very clever one if you use it right, coz hey, who can hate a little girl, and who can blame a dad for wanting to be there for his little girl?...

But the cold hard truth is that he's still in love with her mom and wont or can't admit it.

I would never stay with someone who kept blatantly reminding me that I'm a consolation prize.

Set him free to go chase his first prize, (or his own tail), unless of course you don't mind being second best.