Took mom to a geriatric unit due to hallucinations. She has gone down hill since. Can I take her out of there?

Go get your mama!

You do, almost certainly, if you get MD permission and can care for her. Do understand that your mother may have now had enough, may indeed wish to be released from this hell from which there is no upside coming; get palliative care and hospice consult and speak with them and your mother about her wishes. Please try to honor her wishes. I am so sorry you are going through this.

She has been there for 10 days and they have done evaluations and have her on Zoloft. It is not helping. Parkinson's patients get to this point and even her PD doctor has said she may be at a point where no meds will help the hallucinations. Told us at her last appointment to cherish the next 2-3 months because she is at the end stage. We are a very close knit family and everyone will pitch in to help. We just don't want her at a place where we are only allowed to visit her from 2pm-4pm 3 days a week and weekends. I live literally right next door to the nursing home she was in and would see her almost everyday for 2-4 hours a day. She needs us close. She begs us every time to please take her home.

How long has she been there? If it's only been a few days or a week, you need to give it more time. Are they adjusting her meds? If so, she needs time to either acclimate to them (or a safe place to change the drug regime if what she has now is not working for her). I think it's the law for places like nursing homes to get psych services involved when patients mention self-harm or suicidal thoughts.

I don't have an answer for the legal aspects or what rights you have. However, I'd suggest not taking her home (I assume you mean yours or her home, not the NH).. unless you are able to care for her 24/7. As in quitting your job or hiring people if you can afford it. If you take her home, she won't want to go back to the NH if it proves to be too much for you to handle. It sounds like she is tired of her body being how it is and not just hating the NH?

Also (and I'm not 100% certain on this), you're risking her stay at the unit not being covered by Medicare-- or whatever insurance she has-- if you check her out AMA, Against Medical Advice.

Just a change in where she is living can cause a decline in people with dementia.
Have you considered Hospice?
You could discuss discharge with the doctors but will you be able to care for her at home? Do you have the equipment needed? Although if she were on Hospice they would provide the supplies needed for you to care for her. But do you have help? If on Hospice she would have a CNA that would come 2 or 3 times a week to bathe and dress her, a Nurse at least 1 time a week to check her and order any medications necessary. And you would also have the ability to have the services of a Social Worker, Chaplain as well as other therapies and volunteers if you like.
If she truly wishes to harm herself though she is where she should be. (although personally I understand her statement and wishes)