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
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.