Is it permissible for a wife to leave her house without her husband's permission if she knows that he would give her permission?

The fundamental principle is that a woman is not permitted to leave her husband's house except with his permission, as stated by Sheikh al-Islam Ibn Taymiyyah. However, this permission can be explicit or implicit. If it is customary for him to allow her to go to a certain place, or if she predominantly believes he approves based on an indication, then there is no sin upon her for going out. Thus, the questioner has not committed anything unlawful.