All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Him, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If the daughter possesses any lawful money other than the salary she receives from the bank, there is room for granting permission. If she does not, however, we should consider the condition of the mother. If the lady is poor and needy, there will be no sin on her in taking the money and she can then spend it on whatever she likes of her needs. If she is wealthy, it will not be permissible for her to accept the money in normal circumstances, let alone for [a religious purpose such as] Hajj or ‘Umrah. That is because this money is ill-gotten, and it is not permissible to take gifts, donations or the like, from one whose income is entirely unlawful.
Allaah Knows best.