Mom wants to go to her home for the day, should I take her?

I think it may be too confusing for her... Are you living in her home now? Have you changed it much? Does her bedroom still look the same?

Have you decorated her room at the NH with items from her home so it seems familiar?

When my Mom makes such a comment about wanting to go home, I tell her she is in her home. Mom's bedroom at the NH has her furniture and familiar pieces, and this has really helped.

I think it will only confuse/anger your mom more to experience her "dream" for a day and then have it taken away again. I think a meltdown when you take her back to the nursing facility would be awful and hard on you and I bet that's why you're feeling uncomfortable with the idea. (That's how I'd feel anyway). I agree with Perseverance, make sure she has familiar things around her as much as possible. Just be vague about when/if she might be able to go home. I'm assuming she needs the care of the nursing facility and will continue to be there for the foreseeable future?

Could you take her for an outing somewhere else, like to a restaurant for a meal or for a walk in the sunshine or to a garden or farmer's market, or somewhere else she might like, just to get her out to break the monotony of the facility?

I agree with above. An outing might me better compromise. It is so sad when they want to go home and it is so hard to lie or dissuade when it seems like a simple request. I think it will just make it harder when she goes back to NH. I agree to decorate NH as much as possible with her favorite chair rug, pillows, pictures, etc.

You might consider making a video of the neighborhood, favorite church, garden, even the home that you can show her if you think it wouldn't be to painful for her. Or take pics and assemble in a book she can look thru.