What is the Islamic mode of reconciliation in a situation where a couple, married for 3 years, had an argument and the wife was sent back to her parents' house by the husband?
Problems and difficulties will naturally occur between a husband and a wife, but the commitment to one another must stay as strong as ever. There are shallow problems, and issues, that should be overlooked, with patience, forgiving and forgetting.
However, there are problems that become core issues and cannot be overlooked, like violence, abuse, neglecting religion, drugs, etc. In these cases, seeking consultation and professional assistance is necessary.
You have put effort into the relationship, and have invested a lot into it, so it is very wrong to just throw that away. During an argument and at the heat of the moment maybe things were said that should not have been said, and now that things are calm, one must come back to their original state, and be there for the other.
It is here where one must use their wisdom, moral judgment and religious values. Surrounding people should also try to intervene to minimise the damage.
Islam holds reconciliation in a very high status, and one who aims to reconcile between people has the best of reward. The holy Prophet (s.a.w.) says its reward is more than that of prayer and fasting.
At first, the wife should not have been sent back to her parents' house, because problems must be solved internally, and not by creating more tension by pushing them away. It is for this reason that the husband should show gesture of being genuine and commitment by initiating contact with her and bringing her back home.
Why is it that in many cases the husband/wife could seem to be religious, but when problems arise, they aer far from conducting themselves in the religious way.
The spouse should attempt to reconcile, and other people should also put effort to reconcile. A neutral person from each should can be introduced to arbitrate, so that the issues of dispute are eliminated, and they will no longer have to undergo the same repeated problems. When each party explains their side of the problem, and has a chance to listen to the other side, with wise elders involved the husband/wife will be able to realise where they might have fell short, where their weak/strong points were, and how they can better themselves.
A marriage (Nikah) is a strong covenant, as the Quran says, so stepping away from it should not be taken lightly.
Therefore, the husband and his family should try to approach the wife and her family, and apologise, acknowledge the situation, and bring everything back to normal again.
The husband and wife can involve an arbitrator, and they can agree on certain conditions, but all parties should try as much as possible to reconcile between them.
Try to look at the positive things, forgetting the past and focusing on the future, with a new chapter in your lives, inspired by Allah ta'ala to reform your hearts and bring love and compassion between you.
And Allah knows best.