Don't even contemplate 'sharing' your mum's house with your sister. It willl end in conflict. Don't sign it over because even if she doesn't cause you issues (she's already trying to control you with her suggestion) you can be stitched up in time if she dies and the house passes to her family.
She has her home already and is planning on supplementing her life at your costs. Being a LL isn't a license to print money unless you get some mug to share the pain/take the hit instead.
And yes I know, many, many families get on very well together
But talking from experience. My parents bought their council house with RTB. My dad died and later when the mortgage came to be finished she didn't have the money (they had stupidly gone for interest only). House was valued at £150,000. The mortgage shortfall was £13k. Before I even had a chance to discuss options with her, my brothers first thoughts were how to line his pockets. He offered to buy the house from my mum but for only 75% of the value because he reckoned he'd get 25% as inheritance!
House was too big for her, so I sold the house for her and she moved into a McCarthy and Storm flat fully paid off and £80k in her bank.
Money rules the lives of so many entitled people, who put themselves and their interests way before anyone else. People who you wouldn't think would rip you off can, and do, rip people off for a lot less than the value of your mum's home.
All my siblings actions when she died in 2018 showed where their thoughts really were.