Is a husband entitled to curse, insult, and taunt his wife, and completely boycott her, claiming that the Messenger did so with his wives for the purpose of disciplining them, even after she has apologized and repented for what she has done?

What the wife did by joining a suspicious online activity without her husband's permission is impermissible. However, the husband's cursing, insulting, and taunting her are blameworthy and forbidden by Islamic law, and constitute an act of wickedness. His statement that the Prophet did such a thing to discipline his wives is a lie and a fabrication, for he (peace be upon him) was gentle and merciful towards them. The wife should apologize to her husband and clarify his mistake, then avoid anything that spoils the relationship. If he insists, then good people can mediate between them.