Is it permissible for a son who took care of his father to take the entire inheritance based on the father's will, by which he disinherited his other children due to their disobedience towards him?

You are not permitted to monopolize your father's inheritance to the exclusion of the other heirs based on a will in favor of an heir, as this is forbidden by Islamic law and is not valid unless the other heirs consent. If they do not consent, then the inheritance must be divided according to Islamic law. Disobeying your siblings does not make it permissible to deprive them of their inheritance. Seek your reward from Allah for your dutifulness to your father, and do not squander it by taking something from this fleeting world.