I've been in a similar situation for a year now. I think the reason Nikita acts like that is wise: she's teaching Prince not to even think of trying to push her over like he did to Princess, who now lives in fear of Prince on my bed and has lived so for 1.5 years.
The only thing that has helped mellow Nikita out is for me to lavish reassurance on her. As she becomes more settled with me and the home, she also projects less of her anxiety on Prince.
It's still bad, but not nearly as bad as it was at the beginning.
The key is to reassure the newcomer, in any way that you notice she gains reassurance. Also, if you keep yourself optimistic that this will only improve, your inner calms transmits to the cats and improves things. And remember that cats and their behavior and their dynamics change enormeously with time, and not gradually but in sudden, huge leaps that you never expected.
I used to agonize that I'd have to send Niki back to the streets, so I can understand your feeling.
Adopting a new cat is not easy, it's a challenge to your ability for determination, investment and self-assured optimism. And when one of the huge leaps suddenly occurs, the satisfaction is just too big for words.
The Royal von Meouw Dynasty: His Royal Highness the late Prince von Meouw,
Her Royal Highness Princess Gatita von Meouw, Nikita Duchess of Meouw and
His Highness Cuchi-Cuchi, next in line for the throne of Prince von Meouw.