What is the ruling of Islamic law concerning dealing with a mother who constantly asks for money and gives it to my brother, despite her having sufficient resources, and if I refuse her request, she gets angry, given my desire to buy a house?

You must honor your mother and strive to please her, for her pleasure is from the pleasure of Allah. Her financial support is obligatory upon you if she is in need. If she is not in need, then she has the right to comfort, kindness, and maintaining ties of kinship. The Prophet's (peace be upon him) saying, "You and your wealth belong to your father," is restricted to what does not relate to the son's needs, and on condition that he does not take money from one son to give it to another. The injustice of relatives should be met with patience towards their harm, doing good to them, maintaining ties with them, and forbearance towards them.