It is permitted and praiseworthy to give zakat to needy in-laws, as this entails two virtues: the virtue of charity (sadaqa) and the virtue of strengthening family relations (silat al-rahim), as indicated by the Messenger of Allah (peace and blessings be upon him).
The Messenger of Allah (peace and blessings be upon him) said, “Charity given to relatives has two-fold reward.” [Tabarani, al-Kabir, from Abu Umama (Allah be pleased with him)] He also said (peace and blessings be upon him) to the woman asking him about this that she would have two-fold rewards: “The reward of strengthening family ties, and the reward of charity.” [Tabarani, al-Awsat, from Ibn Mas`ud (Allah be pleased with him)]
Also, it is understood from the Prophetic sunna that one’s family has greater right over one’s charity than others do. In fact, some of the scholars even said that giving zakat to others when one has needy relatives could put the acceptability of one’s zakat in question. While this is not the strongest opinion on the matter, it does highlight the emphasis made in the Prophetic teachings on taking care of the financial needs of family and relatives. [Ibn Abidin, Radd al-Muhtar]
It is only impermissible to give zakat to one’s direct parents, spouse, and children. [ref: Ibn Abidin, Radd al-Muhtar; Mawsuli, al-Ikhtiyar Sharh al-Mukhtar]
And Allah alone gives success.