Is it permissible for a woman to seek khul' from her husband who married another woman to have children, then suffered from depression after her departure, given that there is mutual love and a desire to reconcile, and the father strongly refuses her return?

Obedience to the father is not obligatory in divorcing the wife, and he does not have the right to prevent the husband from returning to his wife, because obedience to the husband has greater right. It is advised to return to the husband and live with him amicably, and to strive to appease the father, seeking help from some relatives to convince him.