Is the daughter's decision to move in with her mother after her parents' divorce—due to the father's ill-treatment, his severing of kinship ties, and his preventing her from visiting and communicating with her mother—correct and appropriate?

If the father does not pray, it is obligatory for the wife to leave him, and it is not permissible for her to return to him, because he is considered a disbeliever, an apostate from the faith, and the marriage contract between them is annulled. Consequently, his guardianship over his children is forfeited, so it is permissible for the daughter to join her mother, and his anger holds no value. Likewise, Sheikh Muhammad ibn Salih al-Uthaymeen holds the view that abandoning prayer after the marriage contract annuls the marriage, and the woman must annul the marriage from a disbelieving husband, because a disbeliever has no guardianship over a believer. This ruling may serve as an incentive for the father to return to his religion and pray.