After wanting my mother's approval (and not getting it) all my life until I was in my late 30's, eventually I stood up to her. Like you, VQ, I had a sister who was the golden one. She could do nothing wrong. I could do nothing right, and when I did succeed in life, I only received grudging approval, or worse still, an embarrassed silence if I had done something better than my (slightly older) sister.
So I wrote her a letter, much easier for me than speaking to her face to face. I said that I felt she did not agree with the way I was living my life and that because of this I did not intend to keep in close touch (weekly phone call, regular letters).
In fact, and completely unexpectedly, VQ, and this is why I am posting this message, I think it did my mother a power of good.
She seemed to blossom, she started to become more sociable, getting involved with village affairs, starting a study programme.
This may have had nothing to do with the shift in our relationship, but I feel that the two were connected. It was as if, in freeing myself, I had freed her also.
We kept in touch but much less frequently.
At her funeral, some years later, I cried. But I cried, not with a sense of loss and grief, but with a sense of relief - that I would no longer have to try and please her.
So, VQ, I understand how deeply these emotional tangles go. But I agree with everyone else who has posted. And I think you may be the most emotionally stable person out of the three of you, even though you are struggling. Because they are struggling just as much if not more so. Try Googling Toxic Families - I read a book on the subject some years ago and it was very helpful.