Is it permissible for a woman to travel after her husband has refused her permission following a dispute, despite his prior consent and the impending filing of a Khul' lawsuit?

As long as the husband has explicitly withdrawn his permission for travel, the wife is not allowed to travel without his permission, and her being in her family's home does not make it permissible for her to do so. It is advised that the spouses reach an understanding to resolve disputes and live together in kindness. If an understanding is not reached, wise individuals from the family or righteous people can be sought to mediate between them, because divorce should only occur when all means of reconciliation have failed. If the spouses are able to reconcile and live together in kindness, even if it means overlooking some minor faults and waiving some rights, that would be preferable to separation.