Praise be to Allah.
Zakaat al-fitr is to be given to the poor and needy, because of the hadeeth of Ibn ‘Abbaas (may Allaah be pleased with him): The Messenger of Allaah (peace and blessings of Allaah be upon him) enjoined zakaat al-fitr as a purification for the fasting person from idle and obscene speech, and to feed the poor. Narrated by Abu Dawood (1609) and Ibn Majaah (1827); classed as hasan by al-Albaani in Saheeh al-Targheeb (1085).
Ibn al-Qayyim (may Allaah have mercy on him) said:
It was his way to single out the poor to receive this charity. End quote.
Zaad al-Ma’aad (2/21).
Having established that, then we know that a poor relative is more entitled to zakaah than anyone else.
But it is not permissible for anyone to give his zakaah to those on whom he is obliged to spend.
You have to spend on them if you would inherit from them. If you would inherit from them then it is not permissible to give them zakaah, but if you would not inherit from them then there is nothing wrong with giving them zakaah.
If you would inherit from some of them and not others, then give zakaah to those from whom you would inherit.
You are not obliged to spend on them unless you have wealth that is surplus to your needs and those of your family. If that is not the case then you are not obliged to spend on them, because you are not able to do so. In that case you may give them your zakaah, even if you would inherit from them.
See also the answer to question no. 106540.
And Allaah knows best.