My friend needs help, so is it permissible for her mother to help her?

There is no harm for a mother to help her daughter with a supererogatory charity (sadaqah mustahabbah); rather, it is commendable, as the Prophet, peace and blessings be upon him, said: "Charity given to the poor is a single charity, while charity given to a relative is two: charity and upholding kinship ties." However, it is not permissible for her to give her zakat money if the daughter is poor, because her maintenance is obligatory upon her wealthy mother, and paying zakat in such a case would negate an obligatory expenditure.