Will a person be rewarded for bringing bread daily to his widowed sister and her children with a sincere intention for the sake of Allah Almighty, and is it permissible for him to make a single intention that everything he spends on anyone is purely for the sake of Allah?

The one who gives charity is rewarded for their charity, especially if it is given to a relative. For charity given to a relative is both charity and the upholding of kinship ties. If the charity is a voluntary one, it is permissible to give it to the rich, though it is preferable to give it to the poor. The reward is attained through the intention when giving it or when delivering it to the poor.