What is the ruling on helping a brother who refuses to work to solve his recurring financial problems, given our mother's insistence on it?

Your previous stance of helping your brother was good, and your current stance of not helping him is correct in order to push him towards self-reliance. Your mother's request for money to give to your brother does not obligate you legally, and her anger towards you because of it will not harm you; for it is without right and you are not obliged to obey her in this matter.

Summary: 1. Continue with your stance towards your brother to motivate him to work, except in cases of extreme necessity that require your direct intervention to pay off his debts. 2. Be gentle with your mother in your refusal, for righteousness and kindness are obligatory. 3. Be patient with your mother's anger, for it will not harm you as long as it is without right. 4. Advise your brother to work and rely on himself, and encourage him with additional financial rewards.