Is it permissible to keep zakat money after the reason for entitlement has ceased (the mother's employment), especially given the existence of debts and fears of the mother stopping work again, and is it permissible to give charity from this money?

If you took Zakat due to your poverty or destitution, you are not obligated to return it if you become self-sufficient before spending it. However, if you took it for a debt that you were unable to repay, and then you became self-sufficient before repaying the debt, then you are obligated to return the Zakat.