You have valid concerns when it comes to how your sister living with you would only make your life harder. The fact that your mother told your sister she could live with you without even asking you is VERY inconsiderate and I am sure that seeing your sister has been living with and so dependent on your parents, they KNOW she is difficult to handle.

Your mother is NOT helping you by putting your sister in your life either, instead her doing that will only end up with you being a codependent to a sister who is irresponsible and needs professional help which is NOT something you have any ability to be for her. You have to sit your mother down and tell her that if she WANTS to help you then she needs to respect the fact that you need to rebuild your life WITHOUT having to be a caretaker like you probably were for your exhusband that pretty much left you having nothing and you NEED to finally have your own life and space to grow as YOUR OWN PERSON, and that means not dealing with ANYONE who will impede that. Help is for YOU to rebuild your life, NOT to be thrown into a living situation with someone who clearly has issues YOU can't fix.