Strongly believe that drama is a cry for attention more than anything else. There is always an issue that sets it off, but in my opinion it's rarely ever about THAT issue. It's a combination of things going on. Everyone has different levels of drama naturally, some people thrive on it, others rarely do it. Either way, in my opinion, it's negative behavior that is oriental to happiness or any positive outcomes.
The real problem is that drama is about attention. Most people, when someone comes at them bitching with drama naturally want to respond with arguments and saying why they aren't at fault. Or they don't like the drama and flat out try to use anger or commands to control it. All of this is attention. When someone acts like this, and you give them ANY attention, you're reinforcing that drama works and they get your attention.
Moreover, drama is never justifiable behavior. Let's say you left a giant mess before you went to work and your wife came home to that mess, and then flew off the handle at you. I think we would agree the husband made a mistake and is "at fault" in this situation. However, if it's met with drama (any harsh, negative emotions directed at you), it's unacceptable. That is neither warranted nor is it an adult way to act. If you screwed up, there are polite, adult ways to discuss that, and then there is drama.
I genuinely think the only option is to completely remove yourself from the situation. Politely of course, but leave. Don't get in a discussion about it, don't argue, just leave. Then later, when you return, you can calmly discuss the issue (if there was an actual source of frustration) like rational adults.