Is a father's obedience, when he objects to a certain matter, despite a positive istikhara and the mother's approval, more worthy than the results of the istikhara? And does the father's objection count as a result of the istikhara, indicating harm in the matter?

There is no contradiction between a father's command and seeking guidance (istikharah), for a father's command may be obligatory. The goodness of a matter is known through istikharah by the broadening of the chest without personal inclination, or by the action or inaction that proceeds from the one seeking guidance thereafter. If there is no hardship or harm for the son in abandoning the command, then obedience to the father in it is obligatory; otherwise, it is not, especially if the father gains no benefit or suffers no harm from the disobedience. Obedience to parents is obligatory in matters that do not involve disobedience [to Allah], that benefit them, and do not harm the son. If it is difficult for him but does not harm him, it is obligatory; otherwise, it is not. As for a mother's mere encouragement, it does not affect the obligation of obedience to the father.