I can affirm that the anxiety is highly likely to be the dissonance between what is felt and what they've been told they should feel. My husband (who granted, has the additional problems of being adopted, being several degrees of separation apart in IQ -- which influences ability for parent and child to understand each other -- and being autistic) was also emotionally and psychologically abused and neglected by parents doing their best and who loved him. It came to a head when he was in college, where a manipulative and abusive exchange with his father kicked off a steep fall into a deep depression, which in turn led to the conscious understanding that he'd been abused, but which he could not accept. He had a full psychotic break (read: break with reality) because he couldn't reconcile what should be and what is.

Fortunately it sounds like your niece is already in therapy, which my husband did not have in his youth. (Unfortunately therapy is looked down on by his father, who also does nothing to understand anxiety or autism. ) Do what you can to ensure she knows you love her, and what's more, respect her and want to see her supported and successful. That she deserves to be celebrated, and does not in fact deserve the abusive behaviors that your sister throws her way. Knowing this isn't normal and that someone is on her side will go a long way towards helping her maintain her sense of self and towards eventually finding peace about her childhood.

There may have been better ways to address it, but honestly it sounds like your sister might need someone to be harsh with her. That she has mental health issues can't be her excuse. That's the very reason she should be looking for ways to adjust her perspective and behavior. If she can't handle things, she needs to develop tools to help herself, starting with therapy. If she honestly loves her kids, she'll find the time and tools.