Is it permissible to give the portion of salary designated for Allah Almighty to a divorced sister who is not being supported, neither she nor her children, and would the reward then be the same?

There is no harm in giving charity to one's sister and her children; rather, it is better, as it combines the reward of charity with maintaining kinship ties. This is in accordance with the Prophet's (peace be upon him) saying: "Charity given to a poor person is charity, and if given to a relative, it is two things: maintaining kinship ties and charity." And his saying: "The upper hand (the one that gives) is better. Begin with those whom you support: your mother, your father, your sister, your brother, then those closest to you, then those next closest."