Caught between 2 sisters - any advice?

It is the sister's house but its also her mother's home as Chewbacca said, it's sad that this feud is affecting a person who was not involved in it. A little kindness and forgiveness would go a long way. It must be very difficult for you being caught in the middle Traviata.

My feedback is this, and it is the most important fact.
It's abuse.

Timing is not irrelevant, in fact, it is the most relevant

If the mother moved in with one of the sisters after the siblings fought and cut off happened, I can see how the mother may be perceived to pick on sister over the other, for example.

Expecting the sisters to "get along and tolerate each other" for the sake of the mother is very unrealistic.

Why is this board so allergic to gathering more facts to give better feedback?

Regardless of any of those details, the mum has the right to have relationships of her own.

How long did the fight between sisters happen
When did your mother move in with one of those sisters?

It's a contravention of a basic human right.
I would be informing the sister of this, and telling her I would be reporting it, unless she changed her stance.

Roses
Because things are not black and white, there are plenty of shades of gray in the middle

I am not happy to condemn the sister who is taking care of the mother without more information.

Roses, I agree. The cause and timeline of the initial fall out between the sisters is irrelevant here. What matters now is that a very elderly, sick lady is being denied access to one of her daughters by the actions of one of them.

Hithere

Why do you need to know these things?

From your description your two sisters fell out, your Mum didn’t fall out with any of her daughters. On that basis you certainly aren’t being unreasonable to believe a visit should happen The choice that was made wasn’t for your Mum to be separated from one of her daughters. As has already been suggested for your Mum’s sake surely the resident sister could go out for a while to enable a visit. Doesn’t have to be a long one. Otherwise, I know this isn’t the same, could anything be done with FaceTime or something similar? This is about your Mum’s needs, not her warring daughters. Having said all that you are in a horrible situation, you sound both physically and emotionally exhausted. I imagine you have anxiety about being banned yourself. Perhaps what is right won’t be able to happen this time, if so please remember it’s not your fault.

Why did the two sisters stopped talking? What created the fight?

How long has been your mother been taken care of by one of those sisters and living at her home?

Your poor mother! How dreadful that she can't see one of her daughters because of a family feud. I agree with both Maddyone and MissAdventure, and perhaps it's time to bang two stupid heads together and remind them that the only person who matters here is Mum.

I have a little experience of a similar situation. Yes, it is your younger sister's house but is also your mother's home too, she just happens to share that home with her daughter. If your mother wants to see her other daughter, and it's reasonable that she would, I think it's rather cruel of younger sister to deny her that in view of her advancing years and declining health. If younger sister feels so strongly about it, perhaps she could go into another room for an hour or so, so that she wouldn't have to see her sibling. Afterall, if your mother was living in her own home, or a nursing home, she would be able to have anyone she wanted to visit her in her declining years. Younger sister is putting her own grievances before the wishes of her elderly mother.

I agree Miss Adventure. A parent who probably doesn’t have a long time to live should be allowed to see her daughter.

When you take someone vulnerable in to share your home, it also becomes theirs, too, so all this "her house, her rules" doesn't wash.

It's abuse. Plain and simple.

Surely if the sister whose house it is could go out for an hour and allow the other sister to visit. Perhaps you could be there to chaperone. Despite it being her house, I really don’t think your sister has the right to deny her sister an occasional visit to her mother.

Of course visits should be allowed!
Not allowing your mum to see family is a huge concern.

I don't think you should get involved. It is your younger sister's house, not your mum's or yours. Your sister has the right to choose who is welcome in her home. What does your mum want?

Sister who has care of your mother is clearly not being kind, but it is her house and she can make her own choices.

What does your mother want?