It would be a good idea to ask the staff a lot of questions about the care she is currently getting, and what they think her needs are. It might also help if you could arrange for her to come home with you for a couple of days, to see how things will go. Many people have found that care at home is far more difficult than they are expecting, and changing your mind won't be easy. Of course that doesn't apply if you are thinking of taking her to another facility. But check the finance agreements carefully - you could find yourself paying for both facilities for three months or more.
Does she have a medical hold? What state is your mother in? If your mom agrees and there are no medical holds you can sign her out. Also depending on the state you live in
You will have to read the power of attorney paperwork. Generally, the person with power of attorney does have the ability to decide where the grantor(your mom) lives. The nursing home has responsibilities also. They must put together a plan for safe discharge before they let her go. Have you spoken to the nursing home staff?
There is also the issue of payment to consider. If your mom's nursing home stay is being covered by any insurance, including Medicaid, you want to proceed carefully to insure that future stays will also be covered should she need them. If you just don't like the place where she is, a lateral transfer to another facility might be something to explore. Just taking her out of the home without exploring how this will affect you all going forward would be a bad idea.
There is also the issue of payment to consider. If your mom's nursing home stay is being covered by any insurance, including Medicaid, you want to proceed carefully to insure that future stays will also be covered should she need them. If you just don't like the place where she is, a lateral transfer to another facility might be something to explore. Just taking her out of the home without exploring how this will affect you all going forward would be a bad idea.