What is the ruling on a woman who desires a khulʿ (divorce initiated by the wife) remaining in the marital home with her children?

Before khulʿ, the wife is under the legal authority of her husband, and she must remain in his home; she is not permitted to leave except with his permission. After khulʿ, which is an irrevocable divorce (ṭalāq bā’in), the wife may reside in the husband's home under certain conditions. A woman is not permitted to request khulʿ unless there is a legitimate Sharʿī justification.