Well, going only by what the OP has told us, and not assuming more, she seems like she's unstable right now[footnote]As if it wasn't obvious enough considering the point of this post.[/footnote].
Letting her back into your life would probably only cause more issues, so it would seem to be a fairly large "Negatory." on that point.
But on the other hand, maybe she'll lighten up a little bit. As one or more people have said, remove the fact that she's your mum, just have the negative and positive qualities of her, as a person, and any and all merits they may bear.
If that alone is enough to make you consider letting her stay[footnote]Which I doubt it will be.[/footnote], then that's peachy. If not[footnote]Which is the most likely case.[/footnote], then kick her out. She doesn't deserve to live there by your description, and by the picture she put in my head, I wouldn't let her stay there, either. Just stop her at the door. If she tries to force her way in, then let her. Just be sure to sneak off, call 911, and hand her over to the cops afterwards. If your past experiences with her aren't enough to condemn her, than work out a plan for her: Make her get a job, and then make her pay for things. Maybe rent, or at least help pay bills, and for groceries etc.