All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Working in banks that deal with Riba (interest and/or usury) is forbidden, as we have clarified in Fataawa 81276, 81665 and 84219.
However, if she is obliged to work in such banks because she could not find any other job to support her mother and sisters, then she may work just for a time enough to pay for the essential needs.
As for the husband's threat, it should not be considered a necessity that makes something unlawful, legal.
Allaah Knows best.