Hi Janis,
It's taken me 58 years to figure out it really is okay to let people choose their own path.
They don't need rescuing unless they look us in the eye and say HELP ME.
(And even then, you've got to carefully coNsider what you know of the source. Don't help Ns to your own detriment!)
I have a friend who frets continually over whether his sibling is controlling or taking advantage of their mother.
I know it is better to let her own whatever fulfillment she finds in it. There's always some inner monologue.
Perhaps it's a maternal dream in some way, that a child --even adult child-- can't comprehend.
Just my thoughts, but you can SAY OUT LOUD to your mother, I am here for you, I am so sorry you are treated so cruelly. Then give a loving hug and ask her out to do something just with you.
After a while, the old Steve Miller song comes to mind: "If you can't be with the one you love, honey, love the one you're with." I'm sure this triangle wasn't on Miller's mind, but in this case, your mother can't "be" with the Ndaughter she loves, because Ndaughter won't allow her to "be."
So maybe your Mom can learn to soak up love from those who do have it to give. Shed the tears over lost Ndaughter when she needs to, then release...and love the ones she's with.
On the other hand, I could visualize a sibling standing up tall in the LR and saying OUT LOUD (without shouting) to the sister, I can't stop you from behaving as you are, but I CAN tell you it is absolutely unacceptable to me to watch you hurting Mom by giving her the silent treatment. Next time I see you I hope you're behaving like a human being.
AND
THEN
LEAVE
love,
Hops
And then leave.