First of all, it's not the Jedi or the Republic she hates. Nor the Sith or the former Sith Empire. What she does despise is the Force. As she studied it, she noticed that it seems to have free will and it's the biggest manipulator in existence. According to her teachings, the Force would play with people, making them do things at it's own will. Remember one line of her dialog where she compares her use of the Force as one would use a poison.
Everything the Exile did, or everything she made the Exile do, was in order that she/he achieved sufficient power to 'kill' the Force. She envisioned on the Exile her own Nietsche superman.