I want this woman I've been telling to move out to leave.
Has she said why she won't leave?
No! She knows I want her to leave, but she just keeps staying around!
If you have asked her politely and the place is in your name, then you are entitled to kick her out. If she won't leave after being firm with her, you should call the police.
She's got to go.
I would suggest being firm with her and giving her a deadline. Tell her that she needs to be moved out by a certain date, and that if she's not you are going to call the police. This way she knows the consequences and can't act surprised if you end up needing the cops to come.