Psychologically, it's much, much easier to be angry at a sibling than at a parent.
But at the end of the day, it's parents who are responsible for shaping family dynamics, not siblings who were children themselves when all this was fermenting.
You seem to see your mother as the victim of your sister, but your sister was originally (and still is in many ways) the victim of your enabler mother as well as your narc father. Neither protected her, prioritised her welfare, just as neither of them truly protected or prioritised you.
If you as the GC have needed bucketloads of therapy I can only imagine what kind of a state your scapegoat sister must be in!
I think it was unreasonable of your mother to copy you all in on your sister's emails in the first place. There's something quite spiteful about that.
I thought it was good you gave yourself permission to feel angry at your mother, and you could probably do with a lot more of that. Your mother set this dynamic in motion. Your mother - agree that she sounds co-dependent - is keeping this dynamic going for her own benefit, however twisted that may appear, not out of real love for your sister. Why aren't you more angry at her for making such a royal hash of being a mother, and still refusing to do anything (like therapy for herself) to become a better one?
I don't honestly know how you can deal with your sister. But if you stop blaming her for your mother's shortcomings, that would be a really good start. And yes, I do think that, consciously or unconsciously, you have been blaming her for other people's failings. Even in your thread title, it's your sister who's the villain of the piece, the problem. That's what happens to the scapegoat. It becomes a kind of family "truth" that they are the root of the problem, to the extent that they can even be "blamed" for things that happened before they were born. And this can somehow seem entirely reasonable and rational.
Your sister's behaviour and emails didn't come out of nowhere. The context has to be acknowledged. If deep down you unconsciously still buy into the myth that she is the source of the family dysfunction, then all your cheerleading for her be a waste of time, she will still not really feel supported by you, and you pushing her to get therapy will just feel like you are confirming that she is the problem, rather than that you are trying to help her get support for her own sake.
Yes, she clearly has some big problems now. But if you can acknowledge that her problems arose out of a situation she did not create, and a situation she still may not have the resources (inner or outer) to tackle, it might help you step back, and give you a different perspective.
You sound like you're taking some really positive steps anyway, and it's refreshing to see someone taking on board so much of what others are saying to you. I just thought I'd stick my two penn'orths in too, in the hope some of it may make sense.