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.
First of all, we thank and praise Allaah Who guided this sister to Islam and we ask Him to make her firm and steadfast on His Religion until the Day she meets Him.
We advise her to seek beneficial knowledge, perform good deeds and befriend righteous and pious women, as these are the best things that help a Muslim woman remain steadfast on her religion.
It is permissible for this sister to ask for divorce from this husband who is an innovator and this is more appropriate for her to do, because staying with him will subject her and her children to be afflicted in their religion. However, she is permitted to stay with him unless he has beliefs that take a person out of the fold of Islam, in which case she is obliged to separate from him.
On the other hand, the fact that the Imaam who conducted her marriage contract was an innovator does not affect the validity of marriage if the marriage contract fulfilled its conditions and if this man’s innovation does not take him out of the fold of Islam.
As regards the fostering of the two children, then it is known that the mother deserves the fostering more than anyone else unless she remarries. If she remarries, the fostering is transferred to the people who are more deserving of their fostering after her, who is her mother, and so forth according to the classification of the most deserving fosterers as clarified in Fatwa 84618.
However, when the children reach the age of distinction, which is seven years old, they are given a choice to choose between their mother and their father, and so, the child remains with the parent whom he chooses unless the latter [parent] is dissolute, because a dissolute person has no right in the fostering of children.
There is no doubt that the two children being fostered by this innovator is more dangerous than being fostered by a dissolute person. Therefore, this husband has no right in fostering those two children.
Allaah Knows best.