My sister(29F) told my(27M) daughters that wife (26F) cheated on me

Backstory is that my wife slept with another guy when she went on a trip for a bachelorette party 2 years ago. Wife got caught after one of her friends sent me a video of wife with another guy. When wife came back she arrived at an empty house. We had a huge argument, she begged me to take her back. The entire family on both sides found out about her cheating. My family was heated, and wanted me to leave her. Ended up staying together for my daughters.

Fast forward 2 years she’s started to gain my trust. Some of the thing I demanded were her phone to be monitored, tracker on her car and phone, no trips allowed without me, just last week I allowed her to go out with her friends for the first time. Before anyone says I’m being way too controlling, these were the conditions I put on the table. If she didn’t want to agree with them or thought they were too harsh I told her divorce was the other opinion.

Last night my older sister was watching the little ones, because we were finishing up some shopping. Apparently my sister told my daughters how my wife was bad and cheated on dad. Wife found out after my younger daughter asked her about her trip to Nashville from 2 years ago. Wife is very upset and has been crying nonstop. I personally didn’t want them to find out through my sister, but I don’t feel as mad or upset as my wife. Wife said that I needed to defend her, and she can’t keep taking this pain. Talked with sister on the phone, and she explained that my daughters asked her why “mommy and daddy weren’t living together for a month”. She said that she told them, because she thought my wife was an awful person. My family hates my wife, but they tolerate her for the kids. My sisters hate my wife with a passion, and don’t even acknowledge her presence. Does my wife have the right to be mad in this situation? How do I handle my wife?