Is what the husband did—expelling his wife from the home and abandoning her for over a year due to her rebelliousness (nushuz), destruction of his property, and neglect of the home and their daughter—considered a divorce, even without uttering explicit words of divorce?

If the wife squanders her husband's money and refuses to share his bed, then she has combined two forbidden acts: squandering his sustenance and committing nushuz (disobedience/rebellion). Nushuz abrogates her right to maintenance and housing, and permits expelling her from the home if she is not pregnant. If she is pregnant, then she is entitled to maintenance and housing. If the husband does not utter the words of divorce, then divorce does not occur.