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.
As for your mother, it is not acceptable to give her any amount from your zakah, neither for her medical treatment nor for her food or clothing because if she is poor or destitute, then spending on her becomes an obligation on you and on her children who are rich, regardless of whether they are males or females.
Ibn Al-Munthir said, "The scholars agreed in a consensus that spending on the poor parents who have no earnings and who have no wealth is an obligation from the wealth of their children.”
If any of the children refuse to spend on her, then they are disobedient to Allaah, The Almighty, and to His Messenger and are being undutiful to their parents and thus commit one of the grave major sins.
Similarly, it is not acceptable to give zakah to your sister – even if she is eligible for zakah – neither in regard to her treatment, food, or clothing, if you are obliged to spend on her.
You are obliged to spend on her if the following three conditions are met:
1- If she is poor and has no wealth or earnings of her own.
2- If you have what you can spend on her in excess of your expenses and your dependents' expenses.
3- If you are one of her heirs when she dies.
This is the view of the Hanbali School, and it is the view that we adopt here in Islamweb.
If any of these conditions is not met, then you are not obliged to spend on her, in which case it is permissible for you to give zakah to her if she is eligible for it.
However, the fact that she owns a piece of land excludes her from being eligible for zakah if she can sell the land and selling it makes her no longer poor in the sense that she would own what would suffice her of food, clothing and her basic needs for a whole year, because whoever owns what suffices him for a whole year is rich and does not deserve zakah.
Ibn ‘Uthaymeen said in Ash-Sharh Al-Mumti’, “…in regard to the chapter on the ruling of giving zakah to the rich [that it is not permissible]; the rich is he who owns his sustenance and the livelihood of his family for a whole year…”
Finally, we should point out that it is an obligation on your rich brothers to fulfill what Allaah has enjoined on them in regard to spending on their mother and sister; which is good for them if they only realize this fact. This is part of dutifulness and keeping ties of kinship, which are both among the greatest acts of worship to Allaah.
Allaah knows best.