Is it permissible for me to give her this zakaah or not?.
The scholars are unanimously agreed that it is not permissible to give obligatory zakaah – which includes sadaqat al-fitr – to those on whom one is obliged to spend, such as parents and children.
It says in al-Mudawwanah (1/344):
What about the zakaah of my wealth – to whom should I not give it according to the view of Maalik?
He said: Maalik said: Do not give it to any of your relatives on whom you are obliged to spend. End quote.
Al-Shaafa’i said in al-Umm (2/87):
He should not give (the zakaah on his wealth) to his father, mother, grandfather or grandmother. End quote.
Ibn Qudaamah said in al-Mughni (2/509):
None of the obligatory zakaah should be given to parents no matter how far the line of ascent goes (i.e., grandfathers and grandmothers) or to children, no matter how far the line of descent goes (i.e., grandchildren).
Ibn al-Mundhir said: The scholars are unanimously agreed that it is not permissible to give zakaah to parents in cases where the giver is obliged to spend on them, because giving zakaah to them will mean that they no longer have any need for his spending on them, and the benefit of that will come back to him, so it is as if he is giving it to himself, and that is not permissible. The same applies if he were to use it to pay off his own debt. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about the ruling on giving zakaat al-fitr to poor relatives.
It is permissible to give zakaat al-fitr and zakaah of one’s wealth to relatives who are poor, and in fact giving it to relatives is better than giving it to strangers because giving it to relatives is both charity and upholding ties of kinship. But that is subject to the condition that giving it is not a means of protecting one’s wealth, i.e., if this poor person is one on whom the rich person is obliged to spend, in this case it is not permissible to meet his needs by giving zakaah, because if he does that he will have saved his own money by giving him zakaah, and this is not permissible. But if he is not obliged to spend on him, then he may give his zakaah to him, and giving zakaah to him is better than giving it to a stranger, because the Prophet (peace and blessings of Allaah be upon him) said: “Your charity given to a relative is both charity and upholding the ties of kinship.” End quote.
Based on this, it is not permissible for you to give your zakaat al-fitr to your mother, rather you should spend on her from wealth other than your zakaah. We ask Allaah to grant you ample provision.
And Allaah knows best.