Is a divorce effective upon uttering the words, "Go to your family, and consider yourself divorced," in a state of extreme anger and with the husband's intention being solely for his wife to go to her family, without intending divorce, after a verbal altercation and the wife initiating insults and shoving?

A husband's words to his wife, such as "Go to your family" or "Consider yourself divorced," are a metaphor for divorce (kinayah talāq). Divorce does not occur with these words unless the husband intended it. Since you did not intend divorce with these phrases, no divorce has occurred for your wife. It is advisable to avoid divorce-related expressions and to use wisdom in dealing with one's wife.