What is the religious ruling regarding the proposed options for solving the problem of a married man who has entered into a customary (urfi) marriage with another woman, feels guilty, and refuses to divorce his first wife?

Marriage without a guardian (wali) is invalid according to the majority of scholars. Therefore, your husband must separate from that woman. However, the marriage is considered valid in some aspects, so she is not permitted to marry another man before her first husband divorces her or a judge annuls the marriage. The child resulting from this marriage is attributed to the husband, and the dower (mahr) and waiting period (iddah) are obligatory. If the husband does not wish to renew the marriage with the guardian's consent, there is no solution other than documenting what occurred between them. It is not permissible for the woman to undergo a hymen repair surgery for the purpose of deceit and fraud, and to expose her private parts ('awrah).