The moment this brother and sister get to know the truth about their relation, their marriage becomes totally null and they must leave each other at once. The reason for this is that the contract is basically null and void, for a brother is prohibited to marry his sister. The evidence for this is the Qur’anic verse that reads: “Forbidden unto you are your mothers, and your daughters, and your sisters, and your father’s sisters, and your mother’s sisters, and your brother’s daughters and your sister’s daughters, and your foster mothers, and your foster sisters, and your mothers-in-law, and your stepdaughters who are under your protection (born) of your women unto whom ye have gone in but if ye have not gone in unto them, then it is no sin for you (to marry their daughters) and the wives of your sons who (spring) from your own loins. And (it is forbidden unto you) that ye should have two sisters together, except what hath already happened (of that nature) in the past. Lo! Allah is ever Forgiving, Merciful.” (An-Nisa’: 23)
However, their previous relationship does not make them liable in the face of Shari`ah (i.e. they are not rendered sinful), for they had cohabitation under a good faith and belief that they were legally married. Islam does not punish people for things they do out of ignorance. However, a Muslim must give up sin the moment he comes to know that it is a sin. Almighty Allah says: “Yet whoso doeth evil or wrongeth his own soul, then seeketh pardon of Allah, will find Allah Forgiving, Merciful.” (An-Nisa’: 110)
As for the children, they are to be ascribed to their father. This is because Allah commands the ascribing of children to their biological fathers. In the Qur’an, we read: “Proclaim their real parentage. That will be more equitable in the sight of Allah.” (Al-Ahzab: 5) However, it is recommended not to mention this relation to the children so as to avoid any future undesired effects.