She sounds unprofessional in her demeanour, bringing ongoing personal issues to work (other than exceptional problems) and this makes you uncomfortable in your own home.
If one is able to come to work then it is appropriate and normal to put on a polite face and greet their employer whatever their personal issues are, and discuss these in an appropriate way if needed, not walk around someones house huffing and puffing.
If your agreement is that she lives out at weekends then she shouldn't be there at weekends, other than by arrangement.
The OP has expressed this in terms of dark energy and sneaking around like a ghost but it is essentially inappropriate behaviour from an employee making her feel uncomfortable in her own home.
Perhaps your depression isn't helping but she is really putting you on edge, with tangible behaviours, not 'bad vibes' such as making personal comments, not showing a civil and professional face in the workplace and hinting at items she wants of yours. Yes, this might be to to with serious issues in her life but quite frankly, that isn't your problem to solve or tiptoe around. As long as you follow.correct practice, you don't owe her a job.
I could be wrong but now you mention the advances and hinting at wanting your stuff, it sounds quite performative, this moodiness. I reckon she thinks she's found a soft spot and is trying to keep you on edge as you're trying so hard to appease her.
As others have suggested, recruit a replacement, check the local laws and give her the appropriate amount of payment in lieu of notice. She's a bad fit, isn't doing a good job and you're well within your rights to try someone else.