Start looking into the laws in your state. There are different laws in different states about eviction, even if that person is not on the lease or mortgage. Often times it is a 31 day notice in writing. You have to have it, again in many states, proven it was given to that person, so registered mail etc. Do this so you have the peace of mind of knowing what that is. Have it written up, and ready to go when you finally have the talk with her, so if it does not go well, you are already locked and loaded, so to speak to protect yourself.
For a very short time I worked in managing apts, in Washington, while they found someone to take that job. I did this as a favor for a family friend of my dad's. When we evicted them, there were laws about holding their things that were left behind as well. We were not able to just sell them or throw them away. We had to package them up and store them, and give them notice on that as well.
I am just talking legalities here. And, I know that is the easiest part of this, as you love your sister.
Keep making the goals in your life, and write them down. Read them. Can you see yourself reaching those goals with this dysfunction in your life?
I think that there are so many wise people on this site with so much more time on under their belt on this than I have. I am just starting this journey.... but I know, through the work I am doing, that we need self care, and if you are not able to achieve that with your sister in your everyday life, with her present, then you need to take that step to bring sanity back into your life.
In the process be kind to yourself.
Blessings....