Is it permissible for the father to forcibly take his child from the custody of the mother after the court has established her unsuitability for care due to health reasons, and that the place is unsuitable for proper upbringing, and given the court's failure to respond to his plea to apply the law in an illegitimate manner?

The just judge, if he rules on a matter of ijtihad (definition) (independent reasoning), it is not permissible to oppose him or for his ruling to be overturned by another judge or by the general public, in order to prevent corruption and block pretexts. It is presumed that such a judge would not rule that the mother's mother is entitled to custody when she is not, for custody considers the best interest of the child.