Is it permissible to give my mother usurious money to get rid of it, knowing that she is the one who covers the household expenses, and that I live with her? Would I then be considered a beneficiary of this money?

If you have usurious gains (ribawi benefits), it is not permissible for you to give them to your mother as long as you are well-off and her maintenance is obligatory upon you, because by doing so, you would be benefiting from them. However, if your mother is in need of money for her essential needs and you are unable to provide for her, then it is permissible for you to give her from those gains.