The story is a bit confusing, so let me see if I can clear it up.

Clara's mom died when she was a child, and since no one knew who her father was, her aunt and uncle took her in. She always felt insecure in the family because of this, and she was afraid that when Charlotte turned 21, she (Clara) would be kicked out of the family. Charlotte didn't trust her and so rewrote her will giving the factory and all the family's wealth to Harper -- which might have been okay, but somehow Clara found out that Charlotte had changed her will, and it terrified her.

The night of Charlotte's 21st birthday party, after the party was over, Charlotte went to the building house where the party was to be held, Clara followed her there and "lit the match." We don't really know what that means; she says she wasn't trying to kill Charlotte, just scare her -- but in any case, the building caught fire and Charlotte died. Clara thinks Charlotte's death was her fault, and Harper thinks so too. And maybe it was.

It's quite possible that Her Interactive left some parts of the story vague on purpose, sometimes to avoid making it really gruesome and sometimes because they like to trigger the creativity of their players. Personally, I think they wrote a Grand Guignol tragedy ghost story and then yanked out half of the plot because it was too gross and horrible for their audience.