All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Islam calls for treating parents with kindness, helping them with both effort and financial means, engaging in polite and respectful conversations with them, and avoiding any expression of frustration or annoyance, especially as they age. Parents require more care than others in acknowledgment of the kindness they provided to their children at young age. Allah, the Most High, Says (What means): "Thy Lord hath decreed that ye worship none but Him, and that ye be kind to parents. Whether one or both of them attain old age in thy life, say not to them a word of contempt, nor repel them, but address them in terms of honour. And, out of kindness, lower to them the wing of humility, and say: "My Lord! bestow on them thy Mercy even as they cherished me in childhood." [Al-Isra`/23-24].
It is established in Islamic Law that the financial responsibility for the parents lies in their wealth if they are self-sufficient. However, if they are in need and do not possess enough to meet their needs, it becomes obligatory for their sons and daughters to provide for them; each according to his/her ability.
Imam Ash-Shirbini (may Allah have mercy on him) stated: "It is obligatory for any person, male or female, to provide for his/her parents... The basis for this is the Saying of Allah (What means): "yet bear them company in this life with justice (and consideration)." [Luqman/15]. Moreover, one aspect of kindness towards parents is to fulfill their needs when they are in need... Ibn Al-Mundhir said: "There is scholarly consensus that the financial responsibility for parents, who have no earnings or wealth, is obligatory from the child's wealth.'" [Mughni Al-Muhtaj, Vol. 15/P. 61].
This is affirmed by the Jordanian Personal Status Law (2019) where Article 197 states: "A solvent child, male or female, adult or minor, is obligated to provide for the needs of their poor parents, even if the parents are able to work."
In conclusion, if the mother, mentioned in the above question, is self-sufficient with the wealth she possesses, her children are not obliged to provide for her needs, and it is not permissible for her to burden her son with expenses beyond her necessities. However, if the mother is poor and has no provider, it is incumbent upon all her children to financially support her, according to their abilities. Each child is obliged to remain kind and obedient to their mother, and won`t be, God willing, and the supplications or anger of the mother do not harm the child if he is dutiful and not neglectful towards her. And Allah The Almighty Knows Best.