I totally agree with several of the posters that regardless of the origin and nature of the dispute between the sisters, this is very definitely abuse. It is a clear example of the coercive control of your Mother.
I also totally understand the motivation behind your attempts at mediation.
Furthermore, I appreciate why suggestions to take your Mother out, telephone or use Skype might not be practical, or achievable.
I totally empathise with your situation and would like to offer the only way, as an impartial advisor, that I can see if persuading your sister, with whom your Mum lives, to relent.
A few people have made reference to the strain your sister is under in caring for your Mum. However close they are and however good, or otherwise, their relationship is, your sister is carrying a heavy burden. If you could suggest that your sister sees supervised visits by your sister to her Mum (preferably by a trusted outsider) as respite, it might be the best way of persuading her to relent?
I truly sympathise with the whole sorry mess and hope some compromise is achieved whilst there is still time...