Actually, Totoro was shown *after* Grave of the Fireflies, at least back in the day. That's why Totoro was remembered forever, considering how uberhappy Totoro was in contrast to the extremely dark Fireflies.
I don't understand why she's crying. I would leap at the chance for a living garbage can I can throw all the people who ever hurt my feelings, pissed me off, or fucked up some aspect of my life and goals, into with no chance of said bodies ever being found.
But then again I'm under the impression that Totoro made her kill them for him to eat them. The gun might be in her hands to protect her, in which case her crying makes sense, seeing as how her imminent death is almost absolutely certain.