Is it permissible for a woman to continue a relationship with a colleague who considers her his wife and intends to marry her, while she is still married to a man who constantly cheats on her? And is this relationship considered betrayal that warrants sin, or should she obey her parents and return to her husband in hopes of his repentance?

If the husband is bad, it is not permissible for the wife to establish an illicit relationship with a foreign man who proposes to her and goes out with her while she is still married to another man. This is a great evil, and she must fear Allah, sever her relationship with him, and repent to Allah Almighty.

If it becomes clear to her that her husband has repented from his evil deeds and desires to live with her in kindness, then she must return to him and live with him in kindness.

However, if he persists in committing evil deeds, it is better for her to separate from him through divorce or khul' (a type of divorce initiated by the wife). If she separates from him and her iddah (waiting period) expires, then she may marry.