Does a son's disobedience to his father regarding visiting his new wife, and limiting his visits to only seeing his children, constitute an act of disobedience (ʿuqūq), or is it a duty towards his mother and a way of protecting her?

Obeying your father and showing him piety are obligatory, and your mother is likewise to be given precedence over him because her right is greater. Obey your father in matters that do not involve neglecting your mother's rights or harming her. Therefore, if a visit does not harm your mother, you are obliged to obey your father regarding it. Your father's wife is one of your mahārim (unmarriageable kin), and she has a right to be shown kindness, as this is part of honoring your father. You are not sinful for not loving her, as love is a matter of the heart.