Does a wife's oath count if she swore to be حرمة (unlawful/forbidden) to her husband that her mother did not insult him, while the husband affirmed hearing the insult, and what is the expiation for that?

A woman's forbidding herself to her husband is neither Dhihar nor divorce. Rather, it necessitates an expiation for breaking an oath (kaffarat yameen). The marital bond between the spouses remains intact. If the mother has indeed disparaged the husband, the wife must offer expiation for her oath. Affection and respect should prevail between the spouses, and they should strive to resolve their issues away from the interference of others.