Does the divorce take effect with the words "You are divorced" when said with the intention of threat upon the occurrence of the suspended act, or is it considered an oath requiring only expiation?

The fatwa we adhere to is that a conditional divorce occurs when the condition is met, whether the intention was to enact the divorce or to threaten. This is the view of the majority of scholars, including the four imams.

Therefore, your divorce has occurred because your wife did what you conditioned her divorce upon. You may reconcile with her during her waiting period ('iddah) if this divorce does not complete the three divorces.

However, according to the view of Sheikh Al-Islam Ibn Taymiyyah, the divorce does not occur if you did not intend divorce by it, but you are liable for an expiation for breaking an oath (kaffarat yamin).