Hi there.
I would appreciate as many responses as possible.

In short, my mom is relying on me to get my sisters to speak with her again.

First to get a quick idea of the family relationship.
It is just me, my mom and two (twins) sister here. The rest of the family lives on another continent. In my teens my mom is in a relationship with a guy I butt heads with every day. And thus I try to get out of the house every moment I can. That plus my sister's having each other, made it so we never got as close as usual siblings I guess.
I left home for good after having enough fighting with my moms bf.

So about 3 years ago, I hosted Christmas eve for me, my mom, two sisters and 2 family friends.
Sometime during the night my mom stated something ( exactly what is unimportant to the story).
I told her I disagreed with her "fact" due to my previous work in a related area. My sister pitched in saying she also thought she was wrong (she was studying something directly to the subject). My mom got annoyed, but stuck to her fact. I asked why she would stick to it rather than actual facts from her daughter who is getting educated in the subject. She gets more annoyed and starts talking about how i wouldn't know because I don't have a social life and stuff like that. (Ive battled anxiety for years but do work. However I acknowledge I relax best at home.)
As she is going on about how I don't have a life I google for the answer and I show her as it backs up me and my sis. She still continues. I shut it down and tell her I don't want to fight and go out for a smoke.
The rest of the evening is tense and when its time for them to leave (sisters live outta town and where staying at my moms) we kinda just acknowledge the fight happened and that we should move on.

About an hour after everyone is gone, my sisters call crying. Asking if they can sleep at my place. I tell them of course. When they arrive I ask what happened. They say that in the car my mom starts talking all kinds of trash about me. They then start defending me and then her anger turns on them.
In the meantime my mom is texting me with some really drunk mean texts. When I respond that we should just leave it for now and talk tomorrow, her answer is "yeah, I don't think so, byyeee".

The morning after my sister's go back to their place and have refused to speak with her ever since.
I spoke with her mainly over text for 3 months before saying we should try and pick up the pieces.

Ever since, our relationship has been rough.
And pretty much every conversation ends up being her talking about how I should fix it and get my sister's talking to her again.

This has resulted in me talking and texting to them over the years, all with the same outcome. Them being annoyed I'm butting in and them not wanting to have any contact with our mom.

And everytime I tell her "I can't fix this. I can't change their thoughts".
I'll ask her what it will take for her to stop putting me in the middle of this?
And always it's just the same.
Ask them if they wanna talk.
....... And it's always no. Not at this time
Ask them why they don't wanna talk.
.......And it's always the same. She won't listen to them.

So after 3 years I think. Okay I'll write them in a way that needs a clear yes or no answer so my mom will stop asking me all the time.

One sister completely stops responding as long as she is the subject.
The other basically states that if she died, it wouldn't bother them.

Sure I was surprised with the blunt answer. But my thoughts went straight to "crap, I gotta tell my mom this".

And I do. Tears turns to anger and back and forth.
And again she keeps asking me to write, call and so on.

It's never ending.

And I've tried explain what I think my sisters mean when they say she doesn't listen.
Aside from above, she will cut you off.
If you say your tired cause you only slept 4 hours, she's only slept 2 hours.

If like now I'm struck with the flu, I should just "pull myself" together and go to that party anyway which I had planned.

So she is counting on me to show up to dinner tomorrow as planned too. Fever in hand.

But she doesn't get it. Sickness is no reason to stay home from work or drinking for her.

Only last week she got a lump looked at which she's had for a month. Now it might turn out to be cancerous. So I had her crying in the phone earlier talking about how none of her kids care about her.
Me mainly because I dint tell my sister that it was f*** up how she replied about her dying.

Maybe I'm in the wrong. My mom keeps talking about how everyone (family and people I've never heard of) keep asking why I don't do something, while those I ask say it ain't my fight.

I've always told my mom I won't go along with her to ambush them at their home.
But now with the crying and the cancer scare I can feel I find it hard to say no when she asks again today.

Yeah I don't know. I just need some guidance from fresh eyes.