I think you have absolutely made the correct decision OP.
Your other children see their sister with so much power in their lives.
Causing angst and grief at every turn.
You are doing your best and she may or may not be willing to be helped.
What you cannot do is sacrifice your other children any further at the alter of her needs.
You have to respect their difficult decision to ask that they take space from her.
She is not entitled to be with them when they actively request that she isn't.
These are the consequences of her behaviour and she will have to hear it and accept it.
You have 100% made the correct decision.
Your mother does not owe your daughter her likely last Christmas either.
I haven't faced this situation so I can only offer a view, but I think that she needs a dose of reality.
That is that people WILL choose to not be around her and will move on with their lives if she continues on this path.
I would not show her any upset or distress.
You have made your decision and are standing by it.
You have more that one child and will make decisions that protect them from her.
She should not be near their birthdays again whilst she behaves like this.
Your other children do not owe her their childhood.
In very very vaguely similar situations where one child was allowed to dominate family life with their poor behaviour, there has been huge resentment towards parents and sibling which has permanently fractured the relationships by causing low contact with the parents.
Let this be the beginning of a new chapter.
You will always love her, but you will now respect your other children's legitimate desire to not be around her and her behaviour.
They have every right to a happy peaceful childhood and memories.
Put your guilt away.
Should it pop up, reflect on the courage it has taken for your other children to spell out that they no longer want to be around her.
Not easy for them to feel and admit.
Wishing you a good Christmas.