I have a question regarding a divorced woman's rights. I moved from a Western country to a Muslim country to marry a Muslim man less than a year ago. I am really unhappy in living in this country because I miss my family and don't feel comfortable enough to have children while my husband wants to have children. I miss my family very much and do not feel happy living here. I need to know what obligations my husband has towards me and what my rights are.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If an inquirer has, by Allah's Favor, a good husband who fulfills all her rights, then she has to be grateful and to avoid seeking divorce, since reproduction is a good quality, not bad as she thinks.
Allah Says (interpretation of meaning): {… and it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. …} [2: 216].
So, offspring constitutes an adornment of this present life as stated in the Holy Qur'an.
In the same vein, the Prophet (Sallallahu Alaihi wa Sallam) said: "When a person dies, his good deeds come to an end except in three cases: …. Or a righteous son who prays for him/her (his father or mother)" [Reported by Imam Muslim ].
Then, the inquirer is not allowed to leave the Muslim countries to live in non-Muslim countries on the plea of longing for her family. The Prophet (Sallallahu Alaihi wa Sallam) said: "I am free from any obligation towards every Muslim who lives among non-Muslims" [Reported by Imams Abu Dawood and al-Tirmizi ].
As for rights of a divorced woman, we state that if she is in the state of revocable divorce, i.e. after consummating the marriage with her, she has the right - during the period of 'Iddah - to receive accommodation and alimony according to the husband's financial state, since she is still under his authority because he can return her as long as she is in her 'Iddah. If the 'Iddah comes to an end, without returning her, her husband is not responsible for accommodation or alimony. If she is in the state of irrevocable divorce and she is pregnant, then she deserves accommodation and alimony for Allah's Statement:
{… And if they are pregnant, then spend on them till they deliver. …} [65: 6].
In Prophetic Hadith concerning the state of Fatimah Bint Qais who was divorced for the third time "There is no alimony for her unless she is pregnant" [ Abu Dawood ]. But, if she was not pregnant, she has no right to receive accommodation or alimony.
In addition, a divorced woman who was slept with has the right to receive both of deferred and prompt Mahr (bridal money) if she did not take it before.
Allah knows best.