My father is very upset with me due to my separating my wife & kids from their house to live with me in a different house to avoid too many fights and arguments which were going on for almost 2 years. My father has stopped talking to me and asked my mother and sisters not to talk to me as well. I always try to keep in touch with them regularly, but my mother hesitates whether she should talk to me or not, and if she does, does this mean that she is disobeying her husband?
Since according to you you had a valid reason for separating, it is wrong for your father to tell your mother not to speak to you. If she speaks to you, she will not be sinning.
Obedience to the husband is only in permissible affairs.
and Allah Ta’ala Knows Best
Ml. Imraan Vawda