What is the correct way to deal with a father who speaks ill of his children and their honor, thinks ill of people, and accuses them of violating others' honor, when they are innocent?

It is not permissible for a father to speak ill of his children. This is considered backbiting, which Allah has forbidden in His saying: "And do not backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allah. Indeed, Allah is Forgiving and Merciful."