Husband told his ex wife our business

Me and my husband are going through a really it. I made some mistakes and I cheated. I feel bad and I eventually came clean. He moved out for a short period and moved back in. We have a child together so we are trying to save our marriage. I found out yesterday that he had gone to the bar his ex wife and mother of his other kids works at. He got drunk and vented about me to her and told her I cheated on him.... I know I'm not allowed to feel some type of way since I cheated but I wish he didn't tell his ex. Me and her don't get along and he just gave her ammo to use against me. He said he was just hurt and needed someone to talk to plus figured we were gonna get divorced so didn't care. I just feel more shame than ever now that she knows.