I don't know about labels such as "splitting" but i certainly know what betrayal is and that's the essence of what your sister has done. She has betrayed you ... big time.
And if what you're saying is accurate / objective she seems like one troubled person who has used both you and your mom to feel some sense of power. Very sick!
I imagine that jealousy got the better of her too.
Also, because she is perhaps more skillful at dealing with the world (like she has a good job, etc.) it's easy for her to point the finger at you. You become the "identified sick one".
But it is you who's in the process of healing. Good for you.
Isn't it amazing how troubled and destructive people can be?
Just stay on your path of healing and avoid people (including family members) who don't support you in that process.
I'm sorry that you lost your mom and that your sister interfered with the reestablished relationship.
I don't know what happens to people when they die but i don't need to know. You can "talk" to your mom now.
You could write her something like a love letter expressing all of your feelings ... both the bad and the good.
You can express anything and everything knowing that, in her heart of hearts, even though she failed you when you were young and wasn't able to properly care for and protect you, she loved you and that love can hear anything that you need to express.
It's not your fault (and i bet i'm right in saying that your mother would agree) that your sister manipulated you.
Don't beat yourself up for that. People can be treacherous!
Thanks for sharing what you did.
I rarely read long posts but i did, for some reason, read yours and i appreciated it very much.
Sorry that you had such a lousy childhood. I did too.