Does the noble Hadith: "Whoever taunts his brother for a sin will not die until he commits it himself" include a wife mentioning to her husband the flaws or character of some people, as a way of informing him of everything she knows, and is that considered a taunt that necessitates the Hadith applying to her?

The hadith (definition) the questioner is referring to has a weak chain of transmission. However, there is a concern that Allah Almighty may punish anyone who taunts or backbites a Muslim by causing them to fall into the very thing they taunted them about, for the recompense is of the same nature as the deed. Muhammad ibn Sirin mentioned that he was punished because he said to a man, "O bankrupt." As for a woman mentioning the faults of others to her husband, it is blameworthy, but it is not taunting; rather, it is forbidden backbiting, for backbiting is "your mentioning your brother with what he dislikes." Moreover, mentioning the faults of others contravenes what the Sharia (definition) has encouraged, which is to conceal a Muslim and defend him.