Is a khul‘ valid religiously if the husband does not agree to it, does not accept compensation, and sees no reason for divorce, especially since the problem was between him and the wife’s family, knowing that the laws in his country do not rule according to Islamic law, and that the wife agreed to return before the judge but her father refused, and she did not declare her hatred for her husband? And is the husband considered to be severing ties of kinship for being unable to visit his son due to the wife's family, despite providing for the maintenance and all the son's needs?

It is not permissible for a woman to seek khul' (divorce at the wife's instance) or divorce without a legitimate Shar'i (Islamic legal) reason. It is forbidden for the wife's family to incite their daughter to disobedience. Her obedience to her husband takes precedence over obedience to her parents when there is a conflict. Rulings of man-made courts regarding divorce or khul' are not considered valid Islamically. You have done well by spending on your son. As for visits, they should be made as much as possible, and if they are impossible, it is not considered severing ties of kinship. If cohabitation with this woman becomes unbearable and attempts at reconciliation fail, then it is better to separate from her through divorce. May Allah grant you someone better than her.