Is it permissible for an adulteress to marry the man with whom she committed adultery, in order to accept repentance and expiate the sin, given that she has a husband and children and it is impossible for them to live together?

Adultery is a grave sin that can only be expiated by sincere repentance that fulfills all its conditions: cessation, remorse, seeking forgiveness, and a firm resolve not to return to it. The sin of a married woman is more severe, but Allah accepts her repentance if she repents and becomes upright. She must conceal herself with Allah's concealment and not expose herself. It is not permissible for her to seek divorce from her husband to marry the one with whom she committed adultery; rather, she must remain with her husband and children and cut off all contact with the one with whom she committed adultery, for the completeness and sincerity of her repentance.