If the reality is as mentioned by the person asking the question, what the father said (Part No. 20; Page No. 289) is Zhihar (a man's likening his wife to an unmarriageable relative). The Kaffarah (expiation) of Zhihar is to free a Muslim slave. If you are unable to do so, you have to fast two successive months. If you are unable to do so, you have to feed sixty needy persons. The following saying of Allah (Exalted be He) indicates this:
And those who make unlawful to them their wives by Zihâr and wish to free themselves from what they uttered, (the penalty) in that case is the freeing of a slave before they touch each other. That is an admonition to you (so that you may not repeat such an ill thing). And Allâh is All-Aware of what you do.
And he who finds not (the money for freeing a slave) must fast two successive months before they both touch each other. And he who is unable to do so, should feed sixty Miskîns (poor).
What you said is a false utterance and ill word from which you should repent to Allah and seek His Forgiveness. Allah (Exalted be He) says,
Those among you who make their wives unlawful to them by (Zihâr; i.e. by saying to them "You are like my mother’s back,") they cannot be their mothers. None can be their mothers except those who gave them birth. And verily, they utter an ill word and a lie.
Allah calls it an ill word and a lie; it is unlawful and requires the person to repent to Allah and seek His Forgiveness. With regards to what the wife said, it is not Zhihar according to the Saying of Allah (Exalted be He),
Those among you who make their wives unlawful to them by (Zihâr الظهار) (i.e. by saying to them "You are like my mother’s back,")
In this verse, Allah addresses the husbands. The wife subsequently has to offer a Kaffarah (expiation) of a broken oath; because whoever makes unlawful what Allah made lawful (Part No. 20; Page No. 290) has to offer the Kaffarah of a broken oath according to the Saying of Allah (Exalted be He),
O Prophet! Why do you forbid (for yourself) that which Allâh has allowed to you, seeking to please your wives? And Allâh is Oft-Forgiving, Most Merciful.
Allâh has already ordained for you (O men) the absolution from your oaths. And Allâh is your Maulâ (Lord, or Master, or Protector) and He is the All-Knower, the All-Wise.
The wife hence has to repent to Allah of this. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.