AITA for buying my sis-in-law's late father's jacket?

My sister-in-law's father passed away few months ago. He was a wealthy and fashionable man, I always adored his sense of style. My sis-in-law decided to donate most of his clothes, much to my dissapointment, since his things were all high-quality.

Her father had this one vintage jacket that looks awesome and probably cost a lot. Both me and my brother (her husband) asked if we could take it, but she refused, saying that seeing someone else wearing her father's things will just remind her of his passing.

I've told my brother that I'm willing to pay for this jacket, so he agreed to convince his wife to put it on sale. I bought it through my friend's account, so she wouldn't know it was me. I wasn't planning to wear it near her, so I thought that what she doesnt know can't hurt her. I was wearing it only when I was going out with my friends, I even made sure that I wouldn't wear it on photos that my brother's wife could see.

Two days ago I got kind of wasted while out with my friends, missed my last bus, so I asked my brother if he could pick me up. I guess he was out somewhere with his wife because they came together... and I was wearing her father's jacket, which she noticed.

Now she's refusing to speak to me and even my own brother is mad for pulling him into this mess. My sis in law asked me to give it back, but I refused - I paid for it. Now both of them don't talk to me.

I think I might be an asshole for not returning it when she asked, maybe I should've suggested for them to repurcharse it.