Is it permissible to marry secretly without the knowledge of the family or official documentation, with witnesses present, for a divorced woman with a daughter, to a married man who proposes to her, due to financial and psychological need and to avoid problems with her ex-husband?

A valid marriage requires the permission of the woman's guardian (wali) and the presence of two witnesses. The guardian is not permitted to prevent the woman from marrying a suitable man unless there is a legitimate Islamic reason. The guardian's refusal to conceal the marriage is justified due to the potential risks and suspicions involved, such as people being unaware that he is your husband or that any child born is legitimately his. You should try to convince the suitor to agree to a publicly declared marriage. If he refuses, it is better to leave him and entrust your affair to Allah. You are not permitted to marry without the permission of your guardian, and such a marriage is not valid according to the preponderant opinion, because the guardian is a condition for the validity of the marriage.