All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Allah the Exalted has legislated for His believing slaves the rulings that insure success and happiness in this worldly life and the Hereafter if they put them into effect.
One of the most important matters the Sharee’ah gives great attention to is marital relations. The Sharee’ah contains many rulings pertaining to the marriage contract before and after it is established and how to solve disagreement if it occurs. The purpose of the Sharee’ah, as confirmed by the Muslim scholars, is either to bring benefits to the people and to complete them, or to protect people from harms and to diminish such harms. So, the Sharee’ah teaches us to reconcile relations between spouses and to send two righteous mediators for this job. However, if it does not work, then one may resort to separation as a last resort though it is not appreciated in Islamic Sharee’ah. The Prophet said: “If any woman asks her husband for divorce without some strong reason, the odour of Paradise will be forbidden for her.” [Abu Daawood, Ibn Maajah, An-Nasaa-i, and At-Tirmithi]
If the disagreement has reached the point that they cannot continue the marriage and the wife is demanding divorce, then a husband can ask for compensation. This kind of separation is called Khul'. Allah Says (what means): {But if you fear that they will not keep [within] the limits of Allah, then there is no blame upon either of them concerning that by which she ransoms herself.} [Quran 2: 229]
Ibn ‘Abbaas narrated that the wife of Thaabit Ibn Qays came to the Prophet and said to him: “O Allah's Messenger! I do not carp at Thaabit concerning his religion or morals, but I fear dishonoring his rights' upon me. Thereupon, the Prophet said: "Will you give him back his garden (i.e. which was given as her bride’s gift)?" She replied: 'Yes’; and she returned it back to him. Then the Prophet ordered Thaabit to divorce her.” [Al-Bukhari]
It is strictly forbidden for the parents or anyone else to interfere in the matters of spouses except for the purpose of making peace between them. So, what your wife's mother did is wrong and not permissible. The Prophet said: “Whoever sows dissension among husband and wife is not one of us.” [Abu Daawood]
Also, it is not permissible for your wife to ask for divorce without any acceptable reason.
Despite the mistakes that are committed by your wife and her mother, our advice is to avoid cursing them though it is permissible in Islam to curse those who are unjust. Allah Says (what means): {Allah does not like the public mention of evil except by one who has been wronged. And ever is Allah Hearing and Knowing.} [Quran 4: 148]
Islam always encourages forgiveness and pardon.
Allah Says (what means):
• {And whoever is patient and forgives - indeed, that is of the matters [requiring] determination.} [Quran 42:43]
• {And to forego it is nearer to righteousness.} [Quran 2:237]
So, do not curse them especially after the divorce has occurred. Know that Allah is not careless about what the unjust are doing.
Allah knows best.