Is the mother obliged to carry out the grandmother's will to divide the inheritance in a way that violates Islamic law and deprives one of the children?

The grandmother's will to divide her estate as she wishes is invalid because Allah's decree takes precedence. She is not permitted to stipulate the deprivation of some heirs or to increase the share of others beyond their legal entitlement, for Allah Himself has ordained the division of inheritances. If she willed the deprivation of some heirs, her will is not to be enforced. If she willed an increase for some beyond their legal share, or a sum of money for your mother, it is not to be enforced except with the consent of the heirs. It is obligatory to advise the grandmother and remind her that injustice in a will is one of the grave sins. What she unjustly willed must not be carried out, whether she retracts her will or not.