What is the ruling of Islam regarding dealing with a wife who seeks divorce in a Western court, refuses Sharia-compliant solutions, considers herself separated from her husband, and acts in a rebellious manner?

The woman mentioned is rebellious (nashiz) and unjust due to her disobedience and non-compliance with the Sharia of Allah, and her belief that the Sharia has not given her justice is an act of disbelief (kufr). The civil court's ruling for divorce is void. A Sharia-compliant divorce can only be effected by the husband or through Islamic centers. The wife is not entitled to a share of the husband's property based on the civil court's ruling. It is recommended to try and reconcile with her, and if she does not respond, the matter should be presented to the scholars at the Islamic center.