What is the ruling on a wife remaining with her ex-husband in the same house under the pretext of caring for her children, and what is the advice of Islamic law in this situation?

Your wife must return to your country, unless she stipulated that you stay with her children. It is not permissible for her to reside in a dwelling where her ex-husband lives, and you are not allowed to approve her in this reprehensible act. You must prevent her; if she does not obey, then she is disobedient (nashiz). Explain to her the right of her Lord and the right of her husband. If she does not become upright, then there is no good in keeping her. It is recommended to divorce a wife if she neglects the rights of Allah or is not chaste, and she cannot be forced; rather, divorcing her may become obligatory.