Is the wife divorced after her travel to China without her husband's knowledge and consent, given that he swore to divorce her three times if she did that? And is she subject to the prohibition with its three divisions, or even four, if she does not resign from her job, and he has broken his oath?

The preponderant view for us regarding the prohibition of a wife is to refer to the husband's intention. If he intended divorce, it is a divorce. If he intended ẓihār, it is ẓihār. If he intended an oath or did not intend anything specific, it is an oath. It appears from the question that the questioner intended divorce by his statement "by three or four." Consequently, his wife has been irrevocably divorced (baynūnah kubrā), and he cannot remarry her unless she marries another man. However, if he did not intend divorce by the prohibition, then the divorce occurred due to the breaking of the other oath, a major irrevocable divorce (baynūnah kubrā), unless he intended emphasis by the repetition, in which case only one divorce occurs, and he can conclude a new marriage contract with her. Some scholars, such as Ibn Taymiyyah, are of the view that a divorce conditioned for the purpose of emphasis or urging does not take effect; rather, it necessitates an expiation for an oath. Due to this difference of opinion, it is advisable to present the matter to trustworthy scholars.