In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If you are unable to pay the treatment expenses of your mother, then there is no harm in paying them from your zakah money.
Answering your question, The Fatwa Center at Islamweb, states:
The basic principle is that it is impermissible for the son to pay his zakah to his parents because he is obliged to provide for them if they are in need. This obligation is not waived by paying his zakah to them.
Ibn Al-Mundhir wrote,
“The scholars unanimously agreed that it is not permissible to give zakah to parents in cases when the giver is obliged to spend on them, because giving zakah to them will mean that they no longer need him to spend on them and that he is spared that duty; so he benefits from it, and it is as if he is giving it to himself (i.e. taking the zakah funds himself), which is impermissible. The is the same as using his zakah to pay off his own debt.”
The wisdom behind the prohibition in this regard is that the child is legislatively obliged to support his poor parents; he cannot pay them the zakah in this case, and this does not waive the obligation of providing for them. However, if the child is financially unable to provide for his poor parents, then it is allowable for him to pay his zakah to his parents in such case.
Ibn Taymiyyah wrote,
“It is permissible to give zakah to one’s parents or children if they are poor and he is financially unable to spend on them. This is one of the two scholarly views reported on the authority of Imam Ahmad. This view is supported by the general religious texts in this regard…”
He also said,
“If they are poor and he is financially unable to provide for them, then the strongest scholarly view in this regard is that it is allowable for him to pay his zakah to them in this case because they are entitled to receive the zakah and the impediment is missing (i.e. payment of the obligatory maintenance to the poor parents). In this case, it is obligatory to act upon the present reason in the absence of a serious impediment…”
Hence, if you are unable to pay the treatment expenses of your mother, then there is no harm in paying them from your zakah money.
Almighty Allah knows best.