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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Adultery is prohibited and one of the grave major sins. It becomes more heinous and greatly sinful if it is practiced with a married woman. So, you must sincerely repent to Allaah and end any relationship with this woman. You have to thank Allaah The Almighty that He kept you alive to repent; otherwise, what would you have done if you had met Him with this sin? Allaah The Almighty Says (what means): {And return [in repentance] to your Lord and submit to Him before the punishment comes upon you; then you will not be helped. And follow the best of what was revealed to you from your Lord before the punishment comes upon you suddenly while you do not perceive, Lest a soul should say, "Oh [how great is] my regret over what I neglected in regard to Allaah and that I was among the mockers."} [Quran 39:54-56] For further information about the conditions of repentance, see Fataawa 86527 and 87903.
As regards the daughter, you have nothing to do with her at all; she should be attributed to the husband of the woman because he is the owner of the bed. The Prophet, sallallaahu ‘alayhi wa sallam, said: "The child is for (i.e. traced back to) the owner of the bed (i.e. the legitimate husband)." [Al-Bukhari and Muslim] For further information see Fatwa 84301. Besides, financial expenses of this daughter and nurturing her are the responsibility of her father. Therefore, you have to break off your relationship completely with this family, so that it would not be a reason to encourage you to commit adultery again with this woman.
On the other hand, if this woman embraces Islam, it would be obligatory for her to separate from her husband, and if her husband becomes a Muslim before her ‘Iddah (waiting period) expires, she will return to him with the first marriage.
However, if he does not embrace Islam until her ‘Iddah has expired, she may marry another man. If you repented to Allaah The Almighty from adultery, you might then marry her with the permission of her guardian and the presence of two witnesses. Were she to have no Muslim guardian, the judge or his deputy in a non-Muslim country would conclude her marriage. For further information, see Fataawa 84226 and 88488.
Allaah Knows best.