بسم الله الرحمن الرحيم
(Fatwa: 1031/809/B=1434)
Your mother is right. First you should pay your debt, and qurbani and zakah shall be wajib when you pay off your debt. After paying the debt if you have money equal to nisab then zakah and qurbani shall be wajib; otherwise not.
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband
