Does divorce by three occur if the wife touches her husband after he says to her: "If you touch me again in the same way (violently), then you are divorced by three"?

If you tied divorce to your wife touching you violently, and she touched you apologetically, then the divorce does not take effect. Anger is from Satan, and moving away from one's wife when angry is wisdom, just as Ali ibn Abi Talib (may Allah be pleased with him) did when he became angry with Fatimah (may Allah be pleased with her) and left the house. It is likely that this was out of fear that he might utter something inappropriate in a state of anger. The wife's attempt to prevent her husband from moving away from her when angry is foolishness and misconduct. Both spouses are advised to seek wisdom and establish foundations for their interaction to ensure family stability.