Is working in a national bank and the money earned from it unlawful (haram), especially with the family's need for money?

If your sister works in an interest-based (riba-based) bank, then her work is forbidden (haram) and her salary is forbidden (haram), and she must leave it unless there is a necessity. However, if she works in a bank that operates according to the rulings of Islamic law (Sharia), then its regulations and her work are permissible (mubah) and her salary is lawful (halal).