Do the aforementioned reasons, namely the desire to maintain the hijab and secure her brother's future, justify taking an interest-based loan to establish a private project in the absence of Islamic banks?

The hijab (definition) is an obligation upon which Muslims have reached a consensus. Preventing a woman who wears hijab from education or work is a law that contradicts Allah's حكم (ruling), and Muslims must reject it. Your father's act of forcing you to remove your hijab is forbidden (محرم), and the hijab takes precedence over education or work. It is not permissible to obey a creature in disobedience to the Creator. Borrowing with usury (riba) is not permissible except in a case of extreme necessity that permits the forbidden, and what was mentioned does not permit usury.