Is it permissible to withhold part of the inheritance from the heirs of my deceased brother—who are adult and of sound mind—claiming fear of their mother's extravagance, or must their full legal share be handed over to them?

The male lineal descendant excludes the collateral relatives from inheriting entirely. So, if all the assets are the inheritance of the deceased brother, the questioner has no right to any part of it due to being excluded by the sons. If the assets were jointly owned, his share returns to his legal heirs, and it is not permissible to dispose of it except with their permission if they are adult and of sound mind. As for the one who is not of sound mind, his guardian is responsible for his money and disposes of it in accordance with what is most beneficial for him.