Is it permissible for the wife to remain in her family's home and refuse to move to the marital home, knowing that the husband owns a private residence and is facing problems with the wife's family?

The wife must obey her husband and preserve his rights, and his marriage to a second wife does not justify her disobedience (nushuz). The husband is not obligated to keep his wife in her family's home unless she is being harmed, and her refusal is considered disobedience. You are bound by what the Shariah judge rules, as the matter is in court, but it is advised not to rush into divorce and to strive for reconciliation to preserve the family and children. It is forbidden to abandon the wife's brothers, and one must initiate greeting them.