It is permissible to give zakaat al-fitr to his wife’s family who are in need
Zakaat al-fitr is to be given to the poor and needy, because Ibn ‘Abbaas (may Allaah be pleased with him) said: 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 talk and obscene speech, and to feed the poor. Narrated by Abu Dawood (1609) and classed as hasan by al-Nawawi in al-Majmoo’ (6/126) and by al-Albaani in Saheeh Abi Dawood.
If your wife’s family are poor and needy then there is nothing wrong with giving zakaat al-fitr to them, rather it is better to give it to them than to anyone else, because the wife’s family (in-laws) have the right to be taken care of as part of honouring one’s wife and treating her kindly.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in Noor ‘ala al-Darb (682):
Undoubtedly the in-laws have rights that no one else has who is not an in-law. End quote.
We hope that Allaah will decree for you the reward for charity and the reward for taking care of your in-laws and treating your wife’s family kindly.
And Allaah knows best.