Praise be to Allah.
If a woman is married, her husband is obliged to spend on her. But if he is in difficulty or he refuses to spend on her, and she is poor and has no wealth, then she may be given zakaah funds.
There is nothing wrong with you giving her some of your zakaah because you are not obliged to spend on her.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (2/279): If the poor woman has a husband who is well off and spends on her, then it is not permissible to give zakaah to her, because she has what she needs from the obligatory maintenance that is spent on her. … But if he does not spend on her, then it is permissible to give it to her. This was stated by Ahmad. End quote.
Al-Nawawi (may Allaah have mercy on him) said in al-Minhaaj: The one who is taken care of by a relative or spouse who spends on him or her is not poor or needy according to the more correct opinion.
Mughni al-Muhtaaj (4/176).
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked: I have a sister who is married and is of modest means. Is it permissible for me to give some of my zakaah to her so as to raise her standard of living and help her to raise her children, especially since her husband does not care about anyone but himself, although we have tried hard to set him straight?
He replied: If she is poor and her husband does not spend on her, and you cannot set him straight, and it is not possible to force him to spend on her, then it is permissible to give her zakaah based on what she needs. End quote from Fataawa al-Shaykh Ibn Baaz (14/269).
Shaykh Ibn Jibreen (may Allaah preserve him) was asked: There is a person who has a niece (his sister’s daughter) who is married to a man who has another wife; can this girl be given zakaah?
He replied: Yes, her maternal uncle may give her zakaah if she is poor and her husband does not spend on her because of poverty or miserliness.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in al-Sharh al-Mumti’ (6/257): With regard to the words ‘Zakaah may not be given to a poor woman who is married to a rich man who spends on her,’
The author stipulated two conditions:
1 – That she should be married to a rich man
2 – That he should spend on her maintenance.
In that case zakaah should not be given to her, because in fact she is not poor, because her husband who spends on her has made her free of need.
But if she is married to a poor man then zakaah is permissible for her and for her husband, because the description (of being poor) is applicable in that case.
If she is married to a rich man, but he is one of the most miserly of people, then she may be given zakaah, because she is poor and has not been made free of need by her husband. So she is included among those mentioned in the verse (interpretation of the meaning): “As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al‑Masaakeen (the poor) …” [al-Tawbah 9:60].
If someone were to ask: Why do you not say to her: Ask your husband and take him to court?
We say: We will not say that to her, because this will lead to problems and it may end up with him divorcing her, which will cause her harm. Undoubtedly meeting her needs so as to ward off this harm is what is enjoined by sharee’ah. End quote.
To sum up: It is permissible to give your zakaah to your maternal aunt if she is poor or needy and her husband does not give her enough.