Haven‘t read it, but plan on doing it someday
Rejected, Shamed, and Blamed: Help and Hope for Adults in the Family Scapegoat Role https://www.amazon.de/dp/B08KHS41K4/ref=cm_sw_r_cp_api_glt_i_81FPSW6EPJWFCCF2C52N?_encoding=UTF8&psc=1
I read an article the author wrote about FSA, you can easily find it, got me a good feel for how the book might be
Also The Body Keeps the Score for CPTSD
So I read this book, Rejected, Shamed, and Blamed: Help and Hope for Adults in the Family Scapegoat Role
And I recall it mentioning why these dynamics happen. The one where your sister, becomes the golden child, and you become the scapegoat.
So to start Narcs are emotionally immature individuals. That's why they are the way they are. When they were young their life experiences lead them to believe being emotional people, or to be in-touch with their emotions was an undesirable/unlovable trait. So this gets ingrained in them over and over again and they eventually lock up their normal emotions, never to see the light again. So they begin to project the version they want the world to see, that be powerful, or smart or logical or whatever. And they project that face at any cost. They are only interested in protecting that image of themselves for themselves, losing that sense of empathy for others.
I've also read that narcs are unable to be empathetic and hate that they can't be. So they hate people who are empathetic because it represents something they can't be.
This gets distorted into hating empathetic traits as a whole. So if their child exhibits those empathetic traits, they scapegoat them. Because they hate those traits and want you to hate that about yourself too. They could also be so afraid of empathy that they just want to shove it away because feelings scare them. So they project this fear of emotions onto the child (who doesn't know any better) and it has the effect of making the scapegoat feel like shit for existing.
When they have a kid who doesn't have these empathetic traits, or rather, a child who is willing to hide their emotions and individuality, they are more likely to end up in the golden child role. Because then the golden child has more in common with the narc parent. Because the golden child has been rewarded for discarding their individuality (just like the narc may have done as a child too). So now they get along because the status quo was met.
I don't know anything about your situation other than what you wrote here. So, take it with a grain of salt, but if your interested in knowing why the narc is the way they are, I think this book would be really good. As well as another book called, Adult Children of Emotionally Immature parents.