Does divorce occur through obsessive thoughts, fantasies, and internal monologues that the husband did not utter, or by the word "tardaha" (he expelled her) which he whispered after imagining that divorce had occurred?

Your statement "I divorced her" was a narration of your brother's words, not an intention on your part to divorce your wife. What happened was a satanic whisper (waswasah) which has no consequence. It is important to be careful about quarrels between spouses and to solve problems wisely.