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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If a husband embraces Islam and he has a non-Muslim wife -other than a woman from the People of the Book- who did not embrace Islam and with whom he consummated the marriage, then the matter depends on her waiting period, if she embraces Islam before the end of her waiting period, the marriage is still valid. However, if she does not embrace Islam and her waiting period finishes, then the marriage contract is nullified and she is not lawful to him unless she embraces Islam. If she embraces Islam and he wishes to marry her, then a new contract has to be signed. Intending to call this woman to Islam or taking care of his daughter is not a sound religious reason to keep this woman as his wife. Allaah Says (which means): {Likewise, hold not the disbelieving women as wives.}[Quran 60:10]. On this regard please refer to Fatwa 89587.
As regards the daughter, since she is mature, she can not be considered as a Muslim like her father. She is upon whichever religion she chooses, and if she opts for another religion than Islam, her father can not be her guardian when she marries. However, he is obliged to spend on her if she is needy according to the view of some scholars as the difference of religion, in their opinion, does not exempt him from his duty to spend on her. Anyway, in general he should be kind to her and call her to Islam as Allaah may guide her to Islam thanks to him.
Allaah Knows best.