At any time after the assumption of control by any of such homes, if the parent or other person, in whom the legal custody of such child would otherwise be, believes such parent or other person entitled to the custody of the child, such person may file a petition in the chancery court of the county in which the home is situated, and set out the facts upon which action is sought, and notice thereof shall be given to such institution, and proof may be taken and the application decided as the chancellor, in the chancellor's sound judgment, may determine, both as to the merits and the adjudication of costs. For this purpose jurisdiction is conferred upon the chancery courts, with the right of appeal.