Is it permissible for a married woman to stop financial aid to her poor family, after her husband had been giving them a monthly sum for 5 years, in order to encourage her adult siblings to rely on themselves and not to be content with abstaining from work like their father, especially since they do not have permanent jobs?

Your action in seeking reform is commendable, and you will be rewarded for it, as long as your brothers find job opportunities and are able to earn a living. As for your father abandoning earning to the point of neglecting his obligatory expenditure, this is not from the religion that Allah approves of, nor is it asceticism. Allah has commanded striving on earth and benefiting from its good things. It is sufficient sin for a person to neglect those whom he is obliged to support.