What is the ruling of the Sharia regarding a marriage whose bonds have been broken by physical abuse and humiliation, exposing the wife to mixing, and slandering her honor, and her desire for divorce to protect herself from falling into the forbidden, while her family considers divorce a disgrace?

A woman is not permitted to seek a divorce except for a valid excuse. If the husband exposes her to free mixing (ikhtilat), neglects her in bed, and beats and insults her without cause, then this permits her to seek a divorce after attempting to mend the situation with him through frank discussion or mediation. As for the family, you must convince them of the seriousness of free mixing, that it angers Allah, and that it is an affront to honor. [You should also convince them] that provision is from Allah. If they are not convinced, then mediate through someone who can convince them of that.