She does not care for herself,as bathing or taking care of her room. She smells bad as does her room with all the junk on floor. I have cleaned it 3 times when she was hospitalized but refuse to do so now. She admits its part of being lazy but she has health issues too. I do not know how to get her to move out as I cannot care for her and my sickly mother. She needs help but refuses to see that.
What's the basis for her living with your mother? Was she supposed to be helping her, or is it just to share costs?
If your mother doesn't need the money, I think you need to have a nice, nonthreatening sit-down discussion with her and explain that she needs more help than can be obtained in her current living situation, and that you have to put your mother as priority.
Set an established reasonable time by which she needs to find other living arrangements. You could even volunteer (if you think it would help) to get lists of places she can go to, as I suspect from what you write that she isn't going to make much effort.
There's a safety issue as well; her lack of care could affect your mother if her hygiene and mess create fall and health hazards.