Will the mother be sinful if she stops financial aid to a family that has been receiving it for five years and whose circumstances have improved, and redirects this aid to another family in greater need, without informing the donor?

Whoever is entrusted with delivering a financial charity to a specific entity, it is obligatory for him to deliver it to that entity. If the entity ceases to exist, or no longer needs the money, then he must return it to its owners or seek their permission to disburse it to other entities. It is not permissible to act on his own discretion without permission. The questioner's mother should inform the donor of the situation, and it is commendable for her to suggest disbursing the amount to another needy family and to apologize for what has passed.