Is it permissible for an apostate wife to return to her Muslim husband after she requested a civil divorce and her adultery was proven, considering there are three children and the possibility of her influencing them? And is it permissible for him to marry her again with a new contract, and what are her rights upon him if she is not permissible for him?

The wife and her mother must repent and return to Islam immediately. If the wife apostatizes, she becomes unlawful for her husband. If she returns to Islam during her iddah (definition) (waiting period), she reverts to him with the same marriage contract. Otherwise, a new contract is required. There is no maintenance for an apostate woman during her iddah. She is entitled to the full mahr (dowry) if the apostasy occurred after consummation; otherwise, there is no mahr. Her custody of her children is forfeited, and the husband must take them from her or raise them upon faith. Attention must be paid to the danger of residing in lands of disbelief, the impermissibility of seeking divorce except for a legitimate reason, the obligation of a woman to safeguard herself, never abandoning her husband, and not resorting to man-made laws except out of necessity. If a woman apostatizes and her iddah expires, the marital bond between them is severed, and she has no right to maintenance or custody of the children. If she returns to Islam, it is permissible to marry her anew.