Love is power, and jealousy born of love is a very powerful motivator. Jealousy can drive people to kill, and in the right situation it can drive people to die.
Kotori knew that Kamui loved her, but he also loved her brother and she knew that, too. Worse, so did Fuuma.
Kotori never was good at dealing with jealousy. She wanted Kamui to be hers and hers alone, and that couldn't happen. Kotori was as pleased as she was upset when Kamui was sent away. If she couldn't have him alone, why should anyone?
Kotori never claimed to be selfless. If others chose to perceive her that way, well, that was their problem. She was kind, yes, and good hearted, but she was also strong-willed. Kotori had a habit of getting what she wanted.
Kotori wanted to own Kamui.
It's not hard for a dreamgazer, even an incomplete one, to know people's limits. Kotori could only see dreams of people close to her, but that was no problem. Kotori knew just what it would take to keep Fuuma and Kamui apart.
Kotori wished for Fuuma to kill her. It was the only way to keep him away from Kamui forever.