Praise be to Allah.
We ask Allaah to bless you and to join you together in goodness, and to bless you with righteous offspring.
If the matter is as you describe, and your wife’s mother is suffering from psychological problems, and she approved of you at first, then there is no sin on her daughter for going against her and agreeing to marry you, so long as her wali approved.
She has to strive to honour her and to uphold ties of kinship with her, and to maintain a good relationship with her sisters, even if they mistreat her, because ties of kinship are an important matter. The one who upholds ties of kinship is not the one who returns like for like, rather the one who truly upholds ties of kinship is the one who maintains those ties even if his relatives cut him off, as the Prophet (peace and blessings of Allaah be upon him) said.
If there is a conflict between obeying one's parents and obeying one's husband, then obeying one's husband takes precedence, because of the greatness of his rights over his wife. The Prophet (peace and blessings of Allaah be upon him) said: “If I were to command anyone to prostrate to anyone else, I would have commanded women to prostrate to their husbands, because of the rights that Allaah has given them over them.” Narrated by Abu Dawood (2140), al-Tirmidhi (1853) and Ibn Maajah (1853); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Ahmad (19025) and al-Haakim narrated from al-Husayn ibn Muhsin that a paternal aunt of his came to the Prophet (peace and blessings of Allaah be upon him) for something she needed, and when her need had been met, the Prophet (peace and blessings of Allaah be upon him) said to her: “Do you have a husband?” She said: Yes. He said: “How are you with him?” She said: “I do not fall short in giving him his rights except what I am unable to do.” He said: “Pay attention to how you are with him, for he is your paradise and your hell.” Classed as saheeh by al-Albaani in Saheeh al-Targheeb wa’l-Tarheeb (1933).
Imam Ahmad (may Allaah have mercy on him) said concerning a woman who had a husband and a sick mother: Obedience to her husband is more essential than to her mother, unless he gives her permission. Sharh Muntaha al-Iraadaat (3/47).
But your wife should honour her mother as much as she can, and you should help her to do that.
And Allaah knows best.