These are just my speculations so please don't take it as spoilers.
So basically what I'm getting from this is, when the parvis family has 2 daughters, only one of them can manifest her power "naturally", but by resonating they can share the ability with their sisters.
Cosette or whatever her name was is probably also a genuine daughter of the duke. From the prison scene I'm sure that Cosette manifested her power first, and went in to resonate with Keira to show her the spirits.
For Cosette, I can somewhat guess that Keira's grandfather did something to frame her mother, and she did all the bullshits for revenge. Their father (I can't even remember his name lol) after losing Keira realize how he was fooled and contracted the magician dude in order to allow Keira to regress.
Thank you for coming to my ted talk.