@NotAbabysitter What would you normally do for Christmas and what is your own family situation, married, kids, single etc.? I think that might help in deciding how to duck this one.
It's not clear exactly what level of care your mother needs. Is it full on, basic needs, or not much?
If you are single and live alone, have you any close contacts that you could unburden yourself to, maybe they'd have you for Christmas if they are in a position to do so, although TBH I realise this suggestion of "inviting yourself" might not appeal to you.
If you are unable or unwilling to spend Christmas at home by yourself, then you must go away. I can understand completely you not wanting to be at your home even with the door locked and blinds down etc. it's the anxiety of what might happen that is so unsettling.
You have agency. You are showing us that you are NOT prepared to do anything for a person (mother) who abused you. That shows great strength of character. You must follow through now, and even if it costs a whack, consider it a Christmas present to yourself to get away from the situation. The sisters will manage fine without your help. They will have to.
Going forward how are you going to deal with further demands that you chip in with help? Plan ahead for that, this could get more intense as time goes on. If you are in a position to move house/flat make a plan. Go incognito. Sounds dramatic, but it might be the only way to cut contact completely which is what you want. Good luck to you.