Is it permissible to pay Zakat to one's deserving in-laws, and what is the ruling on eating from their food if its source is the Zakat money paid to them?

If your wife's family is poor, they are eligible to receive zakat (definition), and there is no impediment to giving it to them. However, it is disliked to eat from or benefit from money that was given as zakat. The evidence for this dislike is that "whoever gives charity to his child or to a stranger, he should not ride it [the animal given in charity], nor eat from its produce in any way, nor drink from it, and this prohibition is in the sense of dislike."