In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
In his response to your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
Yes, it is permissible to accept zakah from your parents-in-law. This is because your father-in-law is not responsible for your living expenses. In-law relationships do not have any financial implications, they are completely independent one from the other.
Almighty Allah knows best.