Praise be to Allaah.
As soon as a woman embraces Islam and her husband refuses to do likewise, the marriage is annulled and it is not permissible for her to live with him. But she should wait out the length of the ‘iddah period. If he embraces Islam, she may go back to him and the previous marriage contract is still counted as valid, but if he does not embrace Islam before the ‘iddah is over, then they are no longer married. If he subsequently embraces Islam and they want to get back together, a new marriage contract must be drawn up. It is not permissible to continue the marriage on the basis of being kind to him.
Majma’ al-Fiqh al-Islami (Islamic Fiqh Council), p. 43.
The children should follow the Muslim parent, so try your best to get custody of them. May Allaah help us and help you by His kindness and mercy.
Sheikh Muhammed Salih Al-Munajjid