What should we do with the money that comes to us as zakat for my mentally disabled brother, who is not in need and whose wealth reaches the nisab? Is it permissible for us to dispose of it and give it to those who are deserving?

If your brother is wealthy on his own or has someone to provide for him, it is not permissible to give him from Zakat (definition). It is necessary to inform the Zakat giver of this, as the Prophet, peace and blessings be upon him, said: "There is no share in it [Zakat] for the rich, nor for the strong, able-bodied worker," and his saying: "Charity is not permissible for the rich, nor for one who is strong and able-bodied." What was taken from this money must be returned to its owner so that he may disburse it to its rightful recipients, unless he has authorized you to disburse it to those deserving of Zakat.