Is working in usurious banks considered forbidden in light of difficult circumstances and the unavailability of other job opportunities, knowing that the father has a job but it is insufficient to cover expenses, and job opportunities in Islamic banks are unavailable?

Working in usurious banks is unlawful except in cases of necessity. Necessity is defined as the point where an individual faces destruction or near-destruction if they do not partake of the forbidden. Your situation is not considered a state of necessity, so you must leave the job and be patient.