She married an American man who announced his Islam, then he stopped praying and denied that Allah created the heavens. What should she do?
Question

                I am a Muslim from a Gulf state and am married to an American man. He declared his Islam when we married, but now he does not pray and he does not want to talk about anything that has to do with Islam. I have four children and I have taught them a little, but he does not care about anything and he has committed zina. He tells me that I do not mean anything to him at all and he no longer comes close to me. I teach my children the Qur'aan and how to pray, but they asked me: Why do we pray and our father does not pray? One day we sat with my daughter's husband and my husband, and I found out that my husband does not believe that Allah is the one who created the heavens and the earth. I am very afraid to take the decision to divorce because I do not work. My family said to me: You are the one who made this choice, so live your life and decide what is best for you. I have tried a great deal to advise my husband, but he refuses to respond. I have been trying for a year. I know that you will say to me: Why have you decided now? Because I am very worried about the anger of my Lord. I hope you can help me. I weep night and day. I want guidance and the pleasure of my Lord. Please help me.
Praise be to Allah.
    Firstly: 

    We ask Allah to make things easy for you and to give you a 
    way out of hardship and relief from distress. 

    Secondly: 

    It is not permissible for a Muslim woman to remain married to 
    a kaafir, because Allah says (interpretation of the meaning):

    “O you who believe! When believing women come to you as 
    emigrants, examine them; Allaah knows best as to their Faith, then if you 
    ascertain that they are true believers send them not back to the 
    disbelievers. They are not lawful (wives) for the disbelievers nor are the 
    disbelievers lawful (husbands) for them”

    [al-Mumtahanah 60:10]. 

    Although the scholars differed as to whether the one who does 
    not pray is a kaafir or not, they did not differ as to whether the one who 
    denies that Allah created the heavens and the earth is a kaafir. 

    If a Muslim apostatises, his marriage to his Muslim wife is 
    rendered null and void. If he comes back to Islam, then their marriage is 
    reinstated, but if her ‘iddah ends and he is still insisting on apostasy, 
    then she is now in charge of her own affairs and may marry someone else if 
    she wishes. Based on that, if your husband persists in his ways, then the 
    marriage between you is annulled according to sharee’ah and you are no 
    longer his wife. 

    You have to strive to get out of this marriage by whatever 
    means, either by talaaq or khula’ or something else. 

    Beware of making the children a barrier between you and 
    leaving this man. 

    Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have 
    mercy on him) said: 

    Many women -- Allah forbid -- are prevented by the presence 
    of children from seeking annulment of marriage. This is a serious matter. It 
    should be said: Annul the marriage; it is not permissible you to stay with 
    this kaafir who does not pray. Your children will never leave you so long as 
    their father is like this. He has no guardianship over them, because the 
    kaafir can have guardianship over a believer. “And never will Allaah 
    grant to the disbelievers a way (to triumph) over the believers” [al-Nisa’ 
    4:141]. So you and your children cannot be separated. As for this 
    husband, there is nothing good in him. You should forsake this kaafir 
    husband and it is haraam to let him be intimate with you; this is a great 
    evil. End quote. 

    Al-Sharh al-Mumti’ ‘ala Zaad al-Mustaqni’, 
    12/250 

    We advise you to take your case to the Islamic centres in 
    your country and to the Muslims, and ask them for help. They know better 
    than us how to deal with this problem, as they are present in that country. 

    We criticise your family's attitude towards you. We 
    understand from your question that you chose this husband and chose to live 
    with him without your family's approval. This was a great mistake on your 
    part, and you have paid the price for that, but that does not mean that your 
    family should abandon you. Keep getting in touch with them and ask good and 
    wise people among your relatives to mediate between you and them so that 
    they will help you and stand beside you during this difficult time. 

    You should understand that what is happening to you now is 
    the result of previous mistakes, among the greatest of which were getting 
    married and travelling without your family's approval, then choosing to 
    reside in a kaafir state rather than living in a Muslim land. 

    This is the price for living in that doomed land. 

    You have to try to leave that country without delay, and go 
    back to your family and your country; take the children with you and bring 
    them up in Islam, teach them to memorise the Book of Allah, instead of them 
    seeing the bad example that prevents them from following the true path. 

    Hence it is right that you should weep night and day for how 
    you have ended up. But weeping does not achieve any benefit. So hasten to do 
    something and strive to change this situation, by annulling the marriage 
    contract and not letting him be intimate with you, and by returning to your 
    family and your country. 

    We ask Allah to make things easy for you and to protect your 
    religious commitment and to make your children righteous. 

    And Allah knows best.