Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.

 

In both cases either the husband gives permission or not, the wife becomes divorced, because he made the condition that if she does such an act, she is divorced.

 

This is the view of the massive majority of Muslim scholars including Hanafis, Malikis, Shāfiʽis and Hanbalis. Al-Bukhari reported that Nafiʽ asked, “[What if] a man said that his wife was divorced irrevocably if she goes out [of the house]?” Ibn `Umar said, “If she goes out, then she is irrevocably divorced from him. If she does not go out, there is nothing.”

 

Almighty Allah knows best.