I'm going to tell a girl that her sister's death did not give her the right to treat other people like shit
Why does she need to know hurtful things like that?
Because she chose to make others suffer in the arms of grief instead of doing something about it.
While you're right that it's not an excuse to treat people that way, you don't need to be nasty to her back. Everyone mourns in their own way, and this is how she does it even though it's bad. You need to just talk to her calmly about it and let her grieve in healthier ways.
I have to tell her anyways, she needs a wake up call in my opinion.
Sadness is not a way to justify being mean, that is not fair to others. But you can be calm and speak to her about it, but if she rejects this way then just ignore her. Let her grieve and never be nasty.