Prayer for reconciliation between spouses
Question

How sound is the prayer for reconciliation between spouses? It involves praying two rak‘ahs, and in each rak‘ah you recite Soorat al-Faatihah, then recite seven times the verse (interpretation of the meaning): “Perhaps Allah will put, between you and those to whom you have been enemies among them, affection. And Allah is competent, and Allah is Forgiving and Merciful” [al-Mumtahanah 60:7]. After completing the prayer, I recite the dua‘aa’: “O Allah, soften the heart of So-and-so [the husband] son of So-and-so [his mother’s name] towards So-and-so [the wife] daughter of So-and-so [her mother’s name] as You softened iron for Dawood.”
Praise be to Allah.Firstly:
There is nothing in Islamic teaching that is called the prayer for reconciliation between spouses, and the du‘aa’ (supplication) mentioned is not proven. It is not permissible for a person to invent acts of worship, or to attribute to Islamic teaching that which has not been narrated.
Based on that, it is not prescribed to offer a prayer specifically for the purpose of bringing about reconciliation between spouses. Rather this prayer – for the purpose mentioned and in this particular manner – is an innovation and is rejected.
But if someone were to offer the supplication mentioned, or a similar supplication for the same purpose, such as saying, “O Allah, make my husband dear to me and make me dear to him,” and the like, if a woman says that during her regular prayer, whether it is an obligatory or naafil (supererogatory) prayer, there is nothing wrong with that.
Similar to that is if a woman offers supplication outside of prayer, asking Allah to change her husband so he will have a good attitude towards her, reciting this supplication or otherwise, outside of prayer; or if a husband asks Allah to change his wife so that she will have a good attitude towards him, without restricting that supplication to specific verses or a specific prayer, this is something that is prescribed, and there is nothing wrong with it.
Du‘aa’(supplication) is one of the greatest means of attaining what one seeks and being saved from what one fears, but that should be without a specific order or specific prayer.
Secondly:
Bringing about reconciliation between people is something very important in Islamic teachings, and immense reward results from bringing about such reconciliation. By the same token, there are stern warnings against creating division among people. It was narrated from Abu’d-Dardaa’ (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Shall I not tell you something that is better than the status of (voluntary) fasting, prayer and charity?” They said: “Yes.” He said: “Reconciling in a case of discord, for the evil of discord is the shaver.” Narrated by al-Tirmidhi (2509), who said: It was narrated that the Prophet (peace and blessings of Allah be upon him) said: “It is the shaver, and I do not say that it shaves hair, but that it shaves (i.e., destroys) religious commitment.” End quote.
Islamic teaching describes several guidelines that will lead to having a peaceful and sound atmosphere in the home, including the following:

Choosing a good wife.
Making the home a place of remembrance of Allah.
Establishing the laws of Allah in the home.
Teaching the members of the household about Islamic faith and manners.
Continually reciting Soorat al-Baqarah in the home to drive away the Shaytaan from the home.
Not allowing anyone into the home whose religious commitment is not good.
Keeping family secrets.

And there are other means that you may learn from the book: The Muslim Home – 40 Recommendations by Shaykh Muhammad Saalih al-Munajjid.
And Allah knows best.