Does a divorce occur if the wife goes to her sister, based on the husband's statements: "If you go to your sister, it will be, or there will be, your divorce," and his other statement: "If you want to ruin things for yourself, then go to your sister"?

What was understood from your statement to your wife: "If you go to your sister, it will be, or there will be, your divorce" is merely a promise of divorce if she goes to her sister. This promise does not constitute a divorce, nor is it desirable to fulfill it, nor is it binding, as stated in Majmoo‘ al-Fatawa by Ibn Taymiyyah.

Therefore, your wife's going to her sister does not constitute a divorce unless you fulfill your promise and actually divorce her. Likewise, your statement: "If you want to ruin yourself, then go to your sister" also does not constitute a divorce if she goes to her sister, and it might be understood as a promise of divorce. Based on this, the divorce is not enacted if your wife goes to her sister.