All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the matter is as you mentioned that this man commits Zina (adultery) then he has indeed committed a grave major sin. What is even graver than this sin is to believe in the ideology of the sect that denies that the Sunnah is a source of legislation, who are the Quraniyyoon. Denying the Sunnah as a source of legislation is an act of Kufr that takes a person out of the fold of Islam as clarified in Fatwa 91740. Indeed, you did well by separating from him.
For more benefit on how to refute the misguidance of such sect, please refer to Fatwa 81124.
Based on that, this man has no right in the fostering of his children as long as he is in this condition because Islam is a condition that must be met by person to be a fosterer according to the preponderant opinion of the scholars . For more benefit, please refer to Fatwa 90461.
However, you are not permitted to prevent him from seeing his children because the jurists stated that it is not permissible for the spouse who has the right to foster the children to prevent the other spouse from seeing the fostered child (children). Ibn Qudaamah said: “A spouse should not be prevented from seeing the fostered child who is with the other spouse.” But you are not permitted to leave him alone with the children when he comes to see them if it is feared that he will influence them with his misguiding and wrong ideas.
In any case, if the parent apostates, his children are still obliged to be kind and dutiful to him, Allaah Says (what means): {But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness}[Quran 31:15] Moreover, the father is obliged to spend on his children even if he is a non-Muslim. Nonetheless, if his earnings are from ill-gotten money, it is only permissible to eat from it according to the necessity.
On the other hand, if this man’s fiancée seeks your advice, then you are obliged to inform her about him just to the extent to make her avoid him. Nonetheless, some scholars are of the view that you should inform her about him even if she does not seek your advice. You are obliged to inform her even if he had already conducted the marriage contract with her. However, if you fear that you or your children will be harmed by him, then you are not obliged to inform her.
Allaah Knows best.