Should she ask for a divorce from her husband who does not pray regularly and does not give her her rights?
Marriage is one of the signs and blessings of Allaah, in which both spouses find peace, companionship, love and compassion, as well as keeping themselves chaste and producing righteous children to populate the earth in accordance with the laws of Allaah. Allaah says (interpretation of the meaning):
“And among His Signs is this, that He created for you wives from among yourselves, that you may find repose in them, and He has put between you affection and mercy. Verily, in that are indeed signs for a people who reflect”
These are the purposes for which marriage has been prescribed. If these aims are not achieved, then divorce is a means that is permitted in Islam, in order for the spouses to move onto a new marriage in which they may attain the aims and purposes of marriage.
What you have mentioned makes it permissible for you to ask for divorce. Al-Tirmidhi (1187) narrated that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Any woman who asks her husband for a divorce without a reason, the fragrance of Paradise will be forbidden to her.” This hadeeth was classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
The phrase “without a reason” means without any hardship that makes her ask for a separation.
Shaykh Ibn Baaz (may Allaah have mercy on him) said: The wife should behave in a reasonable manner and listen to and obey her husband in that which is right and proper, and she should not ask for a divorce with no reason. If there is a reason, there is nothing wrong with that, such as if he is miserly and does not give her her rights, or he commits a great deal of sin, such as drinking and the like, or if he stays up at night a great deal and neglects her right to intimacy, and other such reasons. These are valid reasons (for divorce). End quote from Fataawa al-Talaaq, p. 264.
Although the reasons that you mention make it permissible for you to ask for divorce, you should think long and hard about this matter before doing it, and pay attention to a number of things:
1 – Hope that he will improve, especially if you move to your own apartment. If you encourage him to pray regularly, perhaps Allaah will grant him a good provision and he will try to please you and give up the things that are upsetting you. Then you would have the reward for being patient and treating him well, and for helping him to change himself. So check yourself and think about your husband. If you hope that he can change, then be patient and seek reward with Allaah, and remember that patience brings relief and success. How many women have put up with their husbands and their bad treatment, then Allaah has changed them and they have become among the best of husbands, who did not forget their wives’ patience and kindness. Allaah says (interpretation of the meaning):
“Repel (the evil) with one which is better (i.e. Allaah orders the faithful believers to be patient at the time of anger, and to excuse those who treat them badly) then verily he, between whom and you there was enmity, (will become) as though he was a close friend.
35. But none is granted it (the above quality) except those who are patient — and none is granted it except the owner of the great portion (of happiness in the Hereafter, i.e., Paradise and of a high moral character) in this world”
[Fussilat 41:34, 35]
The woman can play a great role in reforming her husband and calling him to goodness and success, if she uses wisdom, kindness and good methods. First of all she should focus on religious matters, before physical and material issues. If his religious commitment improves, he will be helped and guided in all his affairs, by Allaah’s leave and grace.
2 – You should think of what your own situation will be if divorce happens. This is something to which no attention is paid at times of anger or when one is put off by one's husband. Rather it needs deep thought. The wise woman may accept a hard life with a husband in whom there is both good and bad, and she may prefer that to being divorced, suffering from loneliness and anxiety and looking for a husband at a time when many women are single and it is difficult for virgins to get married, let alone divorced women.
This varies from one woman to another. A divorced woman may still be sought for her religious commitment, beauty, wealth or lineage.
3 – You should turn to Allaah a great deal and ask Him to guide you and ward off evil from you. Do not make a decision until you have prayed to your Lord for guidance (istikhaarah).
We ask Allaah to help you to do that which is good and right and will lead to success.
And Allaah knows best.