Is the questioner considered to have broken his oath—the utterance of which he doubts—"By divorce, I will never fix my car at your place again" if he took his brother-in-law to the workshop to fix his car, knowing that the car does not belong to the questioner and his brother-in-law will pay the money, and that the questioner had forgotten the oath when he took him there?

It appears the questioner is afflicted with waswas (obsessive whispering), and he must desist from it. His swearing an oath of divorce to himself holds no weight, and his uttering it is doubtful, thus having no effect. Even if it is assumed he uttered the oath of divorce that he would not repair his car with him again, he does not break his oath by another person indicating it, but rather he breaks it by repairing his car with him. What he mentioned does not result in breaking an oath or in divorce.