All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the family of your wife is poor, then they deserve Zakah and there is no problem in giving it to them. However, it is disliked to eat or use the money you paid as Zakah although your Zakah is valid and availing.
Al-Kharashi who is a Maaliki scholar, said: “The one who gives charity to his son or to a stranger may not ride it, eat from its yield or drink from it. The prohibition is to indicate dislike.”
Allaah Knows best.