Did I err in rebuking my wife in front of my friend?

The fundamental principle for anyone who observes an inappropriate action from their brother is to advise them privately, away from the eyes and ears of people. This approach is more conducive to the acceptance of advice and the correction of mistakes. This decorum is required with everyone, and with one's wife, it is even more imperative, given her right to a good companionship from her husband. If this decorum is required during advice, which is fundamentally given gently, without raising one's voice or scolding, then what about rebuking? This should not occur in front of others, nor even in private. Rather, mistakes should be addressed through persuasion, wisdom, good admonition, and argumentation in the best possible manner. The husband should placate his wife and apologize to her for what he has done. He must also know that the gathering of men and women in one place, where they look at each other, is impermissible. Instead, men should sit on one side and women on another.