Does a wife become divorced if infidelity is repeated after the spouses have agreed upon it, or is the husband obligated to offer an expiation for breaking an oath, especially since the husband did not intend divorce at the time of the agreement?

If what happened was a clandestine affair or committing an indecency, then one must repent to God. As for your statement to your wife, "If you do such and such, then you are divorced," and you did not intend divorce by it, then no divorce occurs because it is merely a promise, and no expiation for an oath is required of you. One must not be lenient with divorce pronouncements and should strive to resolve marital problems through other means. Both spouses should improve their relationship with each other.