Is the husband considered disobedient to his mother (عاقًا) if his wife insists on wearing the niqab, despite his mother's objection on the pretext of needing her help with housework, and the mother's threat to expel them from the house? And must the husband compel his wife to remove the niqab in this situation?

If the mother orders her son's wife to remove her niqab in front of non-mahram (definition) men, then she is not to be obeyed. The husband must not compel his wife to do so. He should explain to his mother the religious ruling that the niqab is obligatory, and that there is no contradiction between his wife assisting her mother and her adherence to the niqab. If the mother is not pleased, then the wife has the right to a separate dwelling that safeguards her religion and honor.