Does a divorce occur with the statement "I swear by the three" if the intention behind it was to threaten and instill fear, and then the wife broke her oath and did what was sworn against?

The statement "thrice divorced" is not an explicit declaration of divorce, for an explicit divorce is that which admits no other interpretation than the dissolution of the marital bond. Since what you uttered was an innuendo, divorce does not occur by it unless there was intention and purpose behind it. If you did not intend divorce, and your intention was merely to threaten, then nothing is incumbent upon you, even if your wife did what you conditioned it upon. It must be noted that communication with a non-mahram (definition) woman is impermissible except within the limits prescribed by Islamic law.