Is it permissible to give the expiation for intercourse during menstruation to poor relatives who are not in a state of destitution?

There is no harm in giving expiation (kaffarah (definition)) and zakat (definition) to relatives whose maintenance is not obligatory upon you, provided they are among those eligible to receive it. In fact, they have more right to it than others, based on the saying of the Prophet (peace be upon him): "Charity given to a poor person is one charity, but charity given to a relative is two: charity and strengthening of kinship ties." It is permissible to give expiation for intercourse during menstruation and other expiations and charities to poor family members whose maintenance is not obligatory upon you, based on the Almighty's saying: "Indeed, [prescribed] charities are only for the poor and the needy, and those who work on [collecting] them, and those whose hearts are to be reconciled, and for [freeing] captives, and for those in debt, and for the cause of Allah, and for the wayfarer – a duty imposed by Allah. And Allah is All-Knowing, All-Wise."