What is the ruling on a Muslim woman marrying a non-Muslim, given her unawareness of its permissibility, and what are the consequences regarding divorce and the fate of the two daughters?

The woman must leave this man immediately, because this marriage is fundamentally invalid. Scholars have unanimously agreed on the prohibition of a Muslim woman marrying a non-Muslim, based on the Almighty's saying: "And do not marry polytheists until they believe." Her not knowing this removes the sin from her if she was excusable, but it does not prevent the invalidity of the marriage. As for the two daughters, they are attributed to the man, and their lineage from him is established. They follow the mother in Islam, thus becoming Muslim in accordance with her. This woman must strive to learn the rulings of Islamic law and live in a Muslim environment.