o dear I definitely wanted her to pull the trigger. 
As for the umbrella, ... again, I'm clueless. You must have some notion? Must be something to do with the special black rocks? Some quality about them and movement?
Or how about the perception trick? The son that couldn't be copied because he couldn't be perceived properly by the artist guy. They never came back to that. If they'd solved that one, the impression I had was they might have be able to defend against the paper plane attack. But then in the book, it does not appear anyone has figured out how to defend against these dimensional attacks, since the universe is being destroyed by them.
It really sets up male v female too don't you think? When the human race is weaker, it is more feminine. It is the men who are effective wallfacers and swordholders. It is a man who triggers the cosmic signal. It frustrated me with her no end while reading, but by the end you felt maybe she was right to do as she did. Humanity lived in accordance with its values and dreams. Even if that did lead to early destruction.
That theme of human values resonates throughout the books. The image we have of the civilization that destroys humanity is of a v limited, narrow and controlled one. The person who shoots, has little or no larger concept of what is going on, his mind his open to the Elder, he takes no time to consider the morality of his actions. Also, that civilization seemed to be contemplating a voluntary reduction to a 2D state. It is surviving but at what cost?