Praise be to Allah.
The depression that people feel may be a sickness that needs to be treated and needs referral to specialists; or it may be feelings of distress that may be relieved by doing a lot of acts of worship, remembering Allah, keeping company with good and righteous friends, and keeping busy with beneficial actions. For more information on that please see the answer to questions number 22704, 21515 and 100774.
Whatever the case, Allah has not sent down any disease but He has sent down a cure for it, and there is a remedy for this depression no matter what type it is. The believer should adorn himself with patience and certainty of faith, and he should turn to Allah a great deal and ask of Him, because the keys to goodness are in His hand. How many believing men and women have patiently borne a sickness or calamity or imprisonment, without feeling the need to commit a haraam action. This is the action of people who are discontent with the divine decree and are not patient in accepting what Allah wills; they hasten to rid themselves of what has befallen them by any means, no matter what negative consequences it leads to in this world or the Hereafter.
It is not permissible for a woman to ask her husband for divorce except for a legitimate shar’i reason which prevents her from continuing with him, such as his bad treatment or her being put off by him to the extent that she cannot give him his rights. That is because of the reports narrated by Abu Dawood (2226), al-Tirmidhi (1187) and Ibn Maajah (2055) from Thawbaan (may Allah be pleased with him) who said: The Messenger of Allaah (blessings and peace of Allah be upon him) said: “Any woman who asks her husband for a divorce when it is not absolutely necessary, the fragrance of Paradise will be forbidden to her.”
Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
And it was narrated from ‘Uqbah ibn ‘Aamir (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Those who ask for khula’ are hypocrite women.” Narrated by al-Tabaraani in al-Kabeer (17/339); classed as saheeh by al-Albaani in Saheeh al-Jaami’. No/ 1934.
If we assume that the wife in her state of anger, sickness or depression asked her husband for a divorce, when she calms down she will realize her mistake and ask Allah for forgiveness and apologize to her husband.
If the depression and hardship stem from her relationship with her husband, because of his bad treatment or because she dislikes him, and this is proven by trustworthy people from her family, then they should try to bring about reconciliation and consult the husband with regard to that, so as to reach a solution which will bring the wife out of the state of depression in which she is living.
Our advice to the questioner -- who has mentioned that the reason for her depression is being far away from her family -- is that she should be patient and try to get over this crisis.
Depression -- in most cases -- happens to the person who has too much free time, who is not keeping himself busy with useful work, whether it has to do with matters of the Hereafter or with worldly matters.
Keep yourself busy by doing useful things; join a circle for memorizing the Holy Qur'aan; get to know trustworthy sisters who are religiously committed and of good character, and work with them in doing good deeds.
You can make an agreement with your husband that you can visit your family from time to time, and we also encourage your family to visit you as well.
The husband has to put up with what he may encounter from his wife, and try to support her and help her to get over this crisis. It is essential for the husband, the wife and her family to cooperate so that things may go back to normal.
As for divorce, stop thinking about it and overcome the depression that you are faced with. Seek the help of Allah and call upon Him a great deal.
We ask Allah to set your affairs straight and to help you to do all that is good.
And Allah knows best.