Is it permissible for a widow to dispose of the money sent to her and her orphaned daughters by a benefactor, and what is the ruling on her taking from her daughters' money to give to their needy half-brother from their father's side?

Regarding the first question: If the donor's intention was solely to sponsor the two orphan girls, then the money must be considered theirs. It is permissible for the mother to mix food if it is more beneficial for the orphans' money, and if she is poor, she may take what is reasonable. However, if the donor intended to sponsor the entire family, then she may spend on herself what is reasonable.

Regarding the second question: If the husband's family allocated the money specifically for the two girls, then it is considered part of the orphans' wealth. Any surplus beyond their needs must be preserved, and it is not permissible to give any of it as charity or donations.