Is not communicating with one's mother—who caused marital problems and negatively interfered in life, and who asked not to be contacted—considered severing ties of kinship, thereby incurring Allah's wrath, especially since this distance has led to the stability of the marital life?

You are not permitted to shun or abandon your mother, even if she requests it. You must maintain ties with her, honor her, and treat her kindly. You are not obliged to obey her if it involves disobeying your husband. You are required to provide for her financially if she is in need, and it is appropriate to give her money even if she is not. Be kind to her even if she treats you poorly, and maintain ties with her even if she severs them, and do not despair of reconnecting with her. If she expels you or asks to cut off contact, obey her, then try again later, and involve someone influential with her. Fulfill your duties, and be patient, seeking reward [from Allah].