Her husband reviles Islam and does not pray, but if she gets divorced from him, she will be forced to work and take off her hijab
Question

                I have been married for thirteen years to a husband who is thirty years older than me. The problem is that from the first day, we have not got on at all. I have thought of divorce, but I have three children. I was not religious before, but now – praise be to Allah – I never miss any prayer and I am raising my sons in Islam. Even though we are living in Belgium, praise be to Allah my children speak Arabic well. The problem is that my husband never prays, not even in Ramadan, and he has never entered a mosque in his life, and he always reviles Islam. By Allah, I am fed up with this life, but if I get divorced I will be forced to go out to work and take off my hijab. I have not let him be intimate with me for two months, since I read your fatwa on this website. Now we are living in one house, but it is as if he is not here; we do not speak and we do not sleep in the same room.
Praise be to Allah.
    If your husband reviles Islam and does not pray, then it is 
    not permissible for you to stay married to him, because the one who reviles 
    Islam is a disbeliever according to scholarly consensus, and the one who 
    does not pray out of laziness is also a disbeliever, according to the more 
    correct of the two scholarly opinions. 

    If the marriage contract was done at a time when the husband 
    was not praying or when he was reviling Islam, then the marriage was never 
    valid in the first place. 

    If the status of disbelief came after the marriage contract, 
    and the husband continued in his disbelief until your ‘iddah ended, then you 
    are completely separated from him, and you are not permissible for him 
    except with a new marriage contract, on condition that he repent and come 
    back to Islam. 

    Based on that, it is not permissible for you to let him be 
    intimate with you or to be alone with you; rather he is a non-mahram to you. 
    Complete separation does not depend on him issuing a divorce (talaaq); you 
    are not permissible for him whether he issues a divorce or not. 

    Now you have two options: 

    1.To live with your children in 
    the same house that this husband is living in, on condition that you be 
    separated completely from him and that there be no risk of intimacy 
    occurring, and that you tell him that you are not permissible for him, and 
    that intimacy with him when he is still behaving this way is haraam;

    2.To become completely 
    independent and to look for work and accommodation. Undoubtedly this is 
    better and safer for you; perhaps when you look you will find permissible 
    work where you will not be forced to take off your hijab.

    If the problem is a choice between taking off the hijab and 
    staying with this husband who is not permissible for you, and there is the 
    fear that you may commit forbidden actions with him, then taking off the 
    hijab is less serious, but we hope that you will not be forced to choose one 
    of these two options and that Allah will bless your husband by enabling him 
    to repent and mend his ways, or that you will find a job where you do not 
    have to take off your hijab. There are many ways of earning a living, such 
    as teaching children in your house or their house, or working as a 
    seamstress or typist or translator, or working in an Islamic centre, even if 
    you have to move to another city, or you could go back to a Muslim country. 

    Keep asking Allah may He be exalted, and beseeching Him, and 
    do a lot of righteous deeds. 

    We ask Allah to grant you relief and to take away your worry 
    and distress, and to protect you and your children. 

    And Allah knows best.