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.
We have already issued Fataawa 87169 and 84467 clarifying that it is permissible to give Zakat to a sister provided she is among the categories of people who are eligible for Zakat.
We draw your attention to the following matters:
1- If your sister fulfils her needs and necessities with the money given to her by the government, then Zakat should not be given to her on the pretext that she is poor or destitute because if a person has money to fulfil his needs, he is not considered a poor or destitute person.
2- Her husband is obliged to spend on her children, so he should fear Allaah and fulfil his religious obligation of spending on the children. The Prophet said: "It is enough a sin for a person to stop giving means of sustenance to those whom he is obliged to spend on." [Muslim]
3- If the house where your sister lives is the property of her husband, then she has no right to take half of it or less than a half based on the law (in that country); Allaah Says (what means): {And do not consume one another’s wealth unjustly.}[Quran 2:188]. The Prophet also said: "A Muslim's property [money] is unlawful unless he gives it with his proper consent." [Ahmad]
The law does not render what is forbidden lawful, and can not forbid what is lawful. Therefore, she is not permitted to take anything from his house based on the law.