It's a cruel twist of fate that makes the weapon Gale designed the one that killed Prim and so many other young children. Katniss had doubts about the humanity of the tactic, and then to be confronted with the ramifications of it is nearly unbearable. She knew this kind of weapon was being manufactured. She just never expected her own side would use it to such effect.

Katniss is horrified by the discovery that the deaths of those children and her sister were not caused by Snow. That's right – the people on Snow's side didn't slaughter those children. This atrocity was committed by the rebels she's been fighting alongside.

This passage reveals dual power; both Paylor and Katniss have a certain amount of "authority." That authority is Paylor's to command, and Katniss's to command by "right." Somewhat strangely, the second has to be recognized by the first in order to be obeyed, though. As in, Katniss's power here is conditional on Paylor's power already being established.