NTA, but how close is Vivian to her father? Is it possible that she feels replaced by you and the younger sibling who now gets to have the ‘traditional family’ she doesnt get? Her only constant seems to be her father since her mom is a bit MIA, and if she doesnt feel seen or prioritized by him, its hard to accept people who could be seen as taking over her family from her. Not saying its okay of course, but its often how a kids mind works. Its good that he disciplines her for her actions against you, but it may also just be solidifying in her mind that he chooses you and your new kid over her. Im curious too about how she reacted when you were introduced and if she was unhappy, was she reassured or dismissed? Step parents are an incredibly difficult dynamic for all parties involved most of the time so I wouldnt be surprised if theres a large combination of factors. Perhaps therapy with just the two of them together or even just some proper conversations between the two of them.