Am I obligated to cut ties with my brother, in obedience to my husband, because of my brother's wife's bad manners, knowing that I do not want to sever ties of kinship?

Your brother is one of the relatives (Arham) with whom maintaining ties is obligatory, and severing them is forbidden. His wife's bad character is not an excuse to abandon him. Rather, you can avoid meeting her by communicating via phone or similar means.

Your husband does not have the right to prevent you from maintaining ties with your brother in all aspects. However, he can prevent you from visiting him in his home due to the concern of encountering his wife and any harm that might result from it.