Is the mother's action of dividing the inheritance correct, and is it permissible for her to dispose of the remaining amount without the knowledge of her brothers and sisters?

Bequesting to an heir is forbidden and prohibited by Islamic law, and it is not enforceable unless approved by the adult, sane heirs who are not the beneficiaries of the bequest, based on the Prophet's (peace be upon him) saying: "Indeed, Allah Almighty has given every rightful person their due right, so there is no bequest for an heir." Any bequest to an heir is not enforceable, and whatever was taken from it must be returned to the estate and divided according to Islamic law. However, an adult, sane heir who agrees to the bequest being enforced from their share is permitted to do so.