I think how far she goes in trying to destroy ex-partners is based on power. Pete has the most money and can keep paying for injunctions. That makes the balance of power sort of equal. She has a big press following she can use but he has a moderate press following and money for legal and Claire Powell.She didn’t have children with Alex either and look what happened to him.
Alex and Kieran have much less money. They don't have a huge PR person backing them who also has lawyers on tap. They also don't have media ready to publish any 'threat' or denigrating story unlike KP.
Not sure how Carl will turn out, he seems to have recordings of her drug use and no kids of his own to consider when releasing it and she backed down, so again - a sort of power match.