Aunt in-law issues

My husband and I have been married for 5 years, together 6 1/2. I have always had a wonderful relationship with his whole family. Most people talk about how bad their mothers-in-law are but I hit the jackpot. 
But, about a month and a half ago, I posted something on Facebook and my husband's aunt and her daughter assumed it was targeted at the daughter's size. Yes, she's a big girl, but so am I. The aunt started to complete ignore me, talking to people standing right next to me or the baby I was holding and not acknowledging my presence. I had no idea why. A week later, my mother-in-law came to me and told me why the aunt was upset. She even said that she assumed that post was about the cousin. Even when I told her it wasn't, I still think she thinks that. She and my husband want me to go talk to the aunt, but I don't think she'll listen to me AND I think it's her place to come talk to me. 
I UNINTENTIONALLY hurt them but they INTENTIONALLY hurt me. 
My MIL is scared this will break up the family but I'm not missing any family events, but the aunt is. I see that as her problem. 
Any advice on how to solve this?