Praise be to Allah.
The child – male or female – is obliged to spend on his or her parents, if he or she is well off and they are poor, because the Prophet (blessings and peace of Allah be upon him) said: “Start with those for whom you are responsible, your mother, your father, your sister, your brother, then the next closest and the next closest.” Narrated by an-Nasaa’i (2532).
Ibn al-Mundhir (may Allah have mercy on him) said: The scholars are unanimously agreed that spending on parents who are poor and have no income or wealth is obligatory on the child who has wealth. End quote from al-Mughni (8/169).
In order for this spending on parents to be obligatory, there are two conditions:
Firstly, the parents should be poor with no wealth or income that would make them independent of means and have no need for anyone else to spend on their maintenance.
Secondly: the child should have sufficient wealth to spend on them that is surplus to what he needs for his own maintenance and that of his wife, either from his own wealth or his earnings.
It says in Sharh Muntaha al-Iraadaat (3/238): … when the man who is entitled to zakaah is poor and is unable to earn a living, because spending on the maintenance (of a poor person) is only obligatory by way of help, and the one who is well off has no need of help, and the one who is able to earn a living does not need help…
What he wants to spend on them (the poor) should be surplus to his own needs. This is what is indicated by the words “if it is surplus to his own needs” – that is, the needs of the one who wants to spend – “and the needs of his wife and his slave, for one day and night, including their food, clothing and accommodation,” including both what he already has or what he expects of regular income from crafts, trade, rent or income from a waqf set up for his benefit, and the like.
If he has nothing left over after spending on the maintenance of those mentioned above, then he is not obliged to spend on the poor, because of the marfoo‘ hadith of Jaabir: “If one of you is poor, let him first take care of himself. If he has anything left over, then let him spend on his dependents, then if he has anything left over, let him spend on his relatives.” According to another report: “Start with yourself, then your dependents.” The hadith is saheeh.
That is because the obligation of spending on the poor is by way of helping, and it is not obligatory to offer help when you yourself are in need.…
One who is able to earn a living, so that some of his earnings may be surplus to his needs and he can then spend on his relatives, is to be forced to earn a living so that he can spend on his relatives, because neglecting to take care of them when he is able to do so is like neglecting those who are his dependents, and that is not allowed. End quote.
As you have money surplus to what you need for your own maintenance and that of your wife, then you must spend on your mother, if she does not have wealth or income of her own.
This is not your duty only; rather it is obligatory on all her children, male or female, if they are able to do that.
From the above, you will realise that you must work and earn in order to spend on her, if we assume that you have no wealth (or savings).
If your brother is able to spend on your mother, then you should both work together to do that.
If spending is obligatory on you, then it is not valid to count it as zakaah.
Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (2/269): Nothing of zakaah should be given to parents or children. Ibn al-Mundhir said: The scholars are unanimously agreed that it is not permissible to give zakaah to one’s parents in the case where the one who gives it is obliged to spend on them, because giving them zakaah makes them have no need for him to spend on their maintenance, and if that is waived, he will benefit from that, so it will be as if he gave it to himself.
Similarly, he should not give zakaah to his child. Imam Ahmad said: He should not give zakaah to his parents, or his child, or the son of his son, or his grandfather, or his grandmother, or the son of his daughter. End quote.
You should understand that honouring your mother and treating her kindly is one of the causes of blessing (barakah) and increase of provision, so do not regret what you spend on your mother, for perhaps you will be granted provision because of her. The Prophet (blessings and peace of Allah be upon him) said: “Whoever would like his provision to be increased and his lifespan to be extended, let him uphold ties of kinship.” Narrated by al-Bukhaari (5986) and Muslim (2557).
And Allah knows best.