Is it permissible, Islamically, for a deceased mother to bequeath her gold to her daughters exclusively, to the exclusion of her sons, and how is the gold to be divided if her husband is alive?

A will made out to an heir is not valid unless approved by the other heirs. This is based on the Prophet's (peace be upon him) saying: "Indeed, Allah has given every rightful person his right, so there is no will for an heir." The jurists have reached a consensus on this. If some heirs approve the will while others do not, then it becomes valid for the share of those who approved it. Therefore, the gold, like the rest of the inheritance, is to be divided among the heirs according to their prescribed shares. Whoever wishes to approve the deceased's will regarding their share may do so, and whoever wishes to take their share, that is their right.