Is it permissible for a mother to favor her paralyzed daughter, who was abandoned by her husband and whose relatives refused to help her, in the inheritance by giving her more than her siblings, so as to assist her with the costs of treatment and raising her daughter, especially since the mother owns rented properties and fears for her daughter and granddaughter's destitution after her death?

It is not permissible to discriminate in inheritance for the mother or anyone else, because Allah has specified for each heir their share. Likewise, a mother's bequest to her daughter of anything from her estate is not valid because she is an heir, and there is no bequest for an heir. The mother can gift her daughter something during her lifetime and make it her property. It is permissible to single out this daughter for the gift, to the exclusion of her siblings, due to her need and illness, or for other reasons such as a large family, engagement in knowledge, or to prevent her from immorality.