OK, this is controversial and obviously I am biased, so treat this with a big ole handful of salt.
I agree that there are no 'winners' in a scapegoat/golden child situation. I very much agree that BOTH children are victims of bad parenting. However, I do think the behaviour towards the scapegoat is likely to be felt by the majority of people to be more damaging than the behaviour towards the golden child, because even 'fake recognition' of someone's personhood and self is more affirmative than the utter contempt with which the scapegoat is often treated. (A bit like those psychological effects where if you force yourself to smile and be breezy, your mood does improve a bit).
I also think that the vast majority of people will tend to accept positive reinforcement, even if they know it's not entirely sound. When someone tells us we look good, even if we know it's a bit of a porky, it makes us feel better.
I'm not saying this is black-and-white, and that one party has it easy and one doesn't. I'm definitely not saying life is straightforward for golden children. I'm simply saying that in my opinion, being scapegoated is likely to be more psychologically undermining than being the golden child, on the whole for the majority.
I think the OP sees this - all of her posts suggest that she recognises this, and has spent a great deal of time and energy trying to compensate her sister for what she's suffered. She has shown remarkable fortitude and patience in dealing with behaviour, which tells you that she's not your average, huffy, self-righteous person. I think that behind the apparent argument between posters on this thread there is actually agreement, that the OP isn't solely responsible for 'correcting' the situation. What I would suggest is that the current way that things are isn't 'soluble' at all, and that OP is exhausting herself trying to achieve something that is, in fact, impossible - which is to transform the situation with the family dynamic intact.
Instead, what the OP could do would be to build a united front with her sister against the parents, to affirm her sister's view of the family dynamics, and to ensure that it doesn't continue into the future. Obviously, this is a difficult task for either of them individually, but together they could actually have a big impact. I'm not saying that there needs to be some big confrontation with parents or anything, but there can be a firm decision not to tolerate certain attitudes and behaviours that comes from a place of solidarity together. I would suggest a heart-to-heart conversation about what the OP's sister actually would reasonably need to see from the OP to change this - it could be anything from altering beneficial childcare arrangements through to firmly and gently setting behaviours straight when they occur.
I believe that this validation would then be easier for the OP's sister to take some responsibility for certain behaviours (and for the OP to be able to ask, fairly, that she does so, and to support her through therapy, which she clearly needs). I also think it would make it easier for OP's sister to see that the cycle was broken, and that she could move on.