If the house does need to be sold in order to pay fees, then personally I would not feel bad about ultimately making a deed of variation to share out whatever may eventually be left in the proportions that would have applied before care costs.
E.g. for the sake of simplicity, if the house had been worth say £100K and the savings had amounted to £50K, then I would make a D of V to pass on two thirds to the niece, and the other third to the others.
But as others have said, whatever the will might say about the house is irrelevant while your mother is still alive and her assets are needed to fund her care. I don't think any decision re funding should be based on, or at all affected by, what a will may say. I can see that your sister wants the house to be kept, but this just might not be possible or practicable, and I don't think she should expect you to hang on to it no matter what. She needs to understand and accept that her daughter has no claim at all on anything while your mother is still alive. (easy to say, I know...)
Families and wills can stir up toxic hornets' nests, that's for sure.