What is the ruling of Islamic law concerning a wife who has abandoned the marital home multiple times, unintentionally caused injury to her husband, then neglected him, and communicated with another man; is the husband entitled to separate from her despite her desire to continue the marriage for the sake of the children?

If the wife shows repentance and desires to be righteous, her husband should keep her and live with her honorably. However, if she reverts to forbidden actions or if suspicious behavior appears, then it is better to separate from her. The husband must fulfill his role of guardianship (qawamah), close off avenues of temptation, and uphold Allah's limits in his home by preventing her from suspicious seclusion or mixing, obliging her to dress modestly and discreetly, teaching her matters of her religion, and then having a good opinion of her.