Edit 3: tell the mum you are ****** about the lies and not necessarily end your relationship with your mum and sister but just to say, see u only in Xmas and that's that.
Basically reduce the communication and get together to family gatherings only.
Leave them and get on with your life.
That's what I do. I would be upset that my sibling got a whole house but even more damaging upset about being lied about it.
Detach yourself to the mum and sister and when they come calling you for financial or health related help. Tell them to go do one
You'd lose your Mum over cash? And by the sounds of it the mum has been deceived by sister too.