Is it considered slandering the wife for the husband to speak with his daughter about his suspicion that her mother committed adultery, based on his evidence and doubts? And what is required of the husband to repent from that?

It is not permissible to accuse one's wife of indecency without clear proof. If you accused your wife of adultery to your daughter, then you have committed defamation (qadhf), and you must repent to Allah and inform your daughter that you were lying. If your words were merely suspicion about her, then it is backbiting (gheeba), and you must repent from it. A man should fulfill his right of guardianship (qawamah) over his wife and have a good opinion of her, as a safeguard against the forbidden.