Double post because I'm just that fly.
I really don't think a shouting match is the solution to this, no matter how angry we think we deserve to be. Both sides are coming at the issue with a good amount of knowledge that the other doesn't have; it's pretty easy to imagine there are misconceptions at work all over the place here. Howeve, it's not going to be Yamame that tries to break the feedback loop, half because her vengeful rage has her borderline (if not outright) irrational, and half because she's just plain not wise enough to see what must be done for everyone to come out ahead. That means the onus is on us to work with her, however much she'll try to work against us. If there's one thing that will drive someone in a righteous, vengeful fury further into thinking they're right, it's stringing emotions even higher than they already are, especially when that person is pretty simple to begin with.
EDIT: This is not in criticism of anyone individually, so please don't take it as such. I just can't write everything I want to on breaks due to time.
EDIT 2: ELECTRIC BOOGALOO: I say all this because I think the right way to go has already been pointed out. Our death means further bloodshed, more of her friends killed. She needs to realize this. The problem is that she's not wise enough to get past the homicidal rage to realize it if she remains riled up. If we can get her to calm down, even just a little bit, I think that approach has a much better chance of working than bludgeoning her over the head with it will. It would probably be even better if we could do it using her own mode of thinking: she knows how angry and vicious she was because her friends died, she can imagine what our friends will be like if we go missing for a while, and it won't take them too long to figure out what parties are responsible.