Must the sister seek permission from her brother—who doubts the existence of God, abuses and hits her—and from his wife—who caused discord and the severing of kinship ties—before going to perform 'Umrah?

If a man doubts the existence of God and does not pray, he is in grave danger; because belief in God necessitates absolute certainty, and abandoning prayer is an act of disbelief that expels one from Islam, according to many scholars. Therefore, he must be advised to repent. As for the sister's relationship with him, abandonment should be for the sake of Allah due to his transgression, not for worldly reasons. If her connection with him and his wife brings about a predominant benefit, then she should maintain ties with them and visit them. It does not harm her to seek forgiveness from her brother's wife, for the Prophet, peace and blessings be upon him, said: "Allah increases a servant in honor only if he forgives." However, if maintaining ties corrupts her or leads to harm, then she is not to blame for not visiting, but the matter should not escalate to abandonment. It is not obligatory to seek his forgiveness or his wife's forgiveness before performing Umrah.