Must I continue visiting my in-laws, or should I obey my father, who disowned me after I visited them? And should I believe my mother or my wife regarding a dispute that occurred between them without witnesses?

The Sharia encourages reconciliation and reform among people, considering it one of its greatest objectives. Therefore, you must strive to reconcile your family and in-laws through prayer, then by seeking assistance from people of knowledge and influence. If reconciliation is not achieved, then it is obligatory to obey your father, because his obedience is a duty, unlike maintaining ties with your in-laws. Ask your in-laws to understand the situation and maintain ties with them through other means. Work on reconciling your wife and your mother with wisdom, and the default is that your wife is innocent unless proven otherwise with clear evidence.