All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
The husband is obliged to provide for his wife and young children who have no money; please refer to Fatwa 85361.
It is not permissible for him to be negligent in providing for them otherwise he is sinful. Abdullaah ibn 'Amr narrated that the Prophet said: “It is enough a sin for a person not to provide means of sustenance to those whom he is obliged to support.” [Abu Daawood]
The wife is not obliged to go out to work in order to provide for herself and children, and the husband has no right to force her to do so as clarified in Fatwa 91310.
In principle, it is not permissible for the wife to go out to work without the permission of her husband, but if the husband does not provide the obligatory maintenance due on him, then it becomes permissible for the wife to go out without his permission.
Now, what has to be examined is whether the work involves mixing or abandoning Hijab; if this is the case, it is forbidden for her to take up this job unless she is forced to, and the necessity is to be assessed accordingly. Thus, when her need is fulfilled and she is no longer compelled to work, she must leave that job.
Also, she should avoid mixing with men as much as possible and she should be as keen as possible on wearing Hijab. As regards covering the face, although this is an obligation according to the preferred opinion of the scholars, it is less serious than not covering the rest of the body. For more benefit, please refer to Fatwa 83607.
Finally, it should be mentioned that an adult son is obliged to provide for his mother – if he has money. Ibn Al-Munthir reported the consensus of the scholars that the children are obliged to provide for their parents who have no money and no earnings. As regards providing for one's siblings, there is a difference of opinion among the scholars in regard to the obligation of their brother to provide for them.
Allaah Knows best.