Is it permissible for a mother to write over all her money to her eldest daughter to distribute among her sisters after her death, so as to disinherit one of her sisters?

Inheritance is a right for the heirs according to their proximity to the deceased, and it is not permissible to disinherit any of them. If a person bestows his wealth or part of it during his lifetime, that is valid and enforceable. However, if the gift is made contingent on after death and disposal of it is prohibited before that, then it is a will and not a gift. A will made to an heir is not valid unless the other heirs approve it, based on the hadith (definition): "Indeed, Allah has given every rightful person his right, so there is no will for an heir."