Is it permissible for a widow observing the waiting period (iddah) to contribute to the medical expenses of her mother, given that she is unemployed, has one son, is financially capable, and her brother is a government employee?

A woman being in a mourning period does not affect her financial transactions. Therefore, there is no harm in your participation in the expenses for your mother's treatment. This is an act of filial piety for which reward is hoped, and it may become obligatory for you if your mother is in need and cannot find anyone else to suffice her.