Will I be sinning if I tell my mother about the offer my father made regarding the bank deposit, knowing that my mother will most likely accept the deposit’s interest even if she knows that its interest is usurious?

There is no blame upon you for informing your mother about the deposit if you are sure that a greater harm will not result from it. Informing her would be more appropriate if a preponderant benefit is likely to result. However, if your father asked you to keep it secret, or if you know that he dislikes your mother knowing, then it is not permissible for you to inform her, as that would be disclosing a forbidden secret. As for the benefits of the deposit, they are to be spent on the poor and the needy. If your mother is among them, there is no harm in giving it to her. If she instructs you to use it for yourself without being poor or in need, it is not permissible to obey her in that. Rather, you should gently excuse yourself, for the Prophet, peace and blessings be upon him, said: "There is no obedience in disobedience to Allah; obedience is only in what is good."