Can my mother give to my brother, her son, from my maternal uncle's zakat money, knowing that my uncle would not approve of it, even though my uncle has authorized her to dispose of the money?

It is permissible for the owner of zakat (definition) to appoint someone else to distribute it, and it is permissible for him to specify certain individuals to whom the zakat should be given. In this case, the agent must adhere to the condition set by the principal. However, if your uncle appointed your mother to distribute his zakat money to the poor and needy in general, without specifying individuals by name, then it is permissible for her to give the zakat to her children if they are eligible for it. Therefore, there is no harm in your mother giving to her son, provided he is eligible for zakat.