Who do I owe my zakat to?

I’m obliged to pay zakat this year as I am now earning. I had decided to give the money to someone who took care of my mother before she passed and now this person is seriously ill and is in hospital with a massive bill to pay. She is poor and doesn’t have much money. My husband is now telling me that I shouldn’t be giving the majority of my zakat to my fathers side as I am no longer a daughter of that family but a daughter of my in laws. They are saying that they have poor people that were relying on my zakat. I just wanted to asked is it obligatory for me to prioritise my zakat to my in laws over the lady who helped my mother. I tried to explain to my husband that it’s my zakat and I can choose who it goes to. Please can someone let me know if I am wrong.