How much of our arguments is fair for my wife to tell her sister?

At dinner, my sister-in-law said, "So, did you finally learn where the laundry basket is?" Everyone laughed. My wife and I had argued about the laundry two nights earlier, then worked out that I'd take the towels and sheets. I hadn't known her sister had heard the argument.

Later, my wife said she'd called her sister because she was irritated and wanted to talk. I understand that. I sometimes talk to a friend when we're annoyed with each other too, although I tend to describe the disagreement rather than repeat what she said. We have never agreed on a rule.

What bothered me most was arriving at dinner thinking the argument was settled, then becoming the joke. My wife says the problem was her sister bringing it up, not her telling her. She doesn't want to have to ask permission every time she needs someone outside our marriage to listen.

What would be a reasonable request here? I want her to have support, and I want to sit down with her family without wondering which private conversation has become dinner material.