بسم الله الرحمن الرحيم
(Fatwa: 984/634/L=1434)
Your wife cannot give her zakah to her real mother (your mother-in-law). However, she may give her zakah to your mother provided she is not a Sayyid and she is entitled to receive zakah.
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband
