What do I tell my mom when she calls asking me to come get her and take her to her home?

Six weeks is really not long enough to get used to anything new, First, I would lose the phone. I agree that she may need a med to calm her.

Sounds like Mom has some form of Dementia. You may never be able to make her understand why she can't go home. Just tell her for now, this is where she needs to be. You can discuss going home when the doctor says she is OK. Blame the doctor. Tell a little fib.

Is she upset a lot of the time? I'd discuss it with her doctor to see if she might benefit from medication. My LO suffered with a lot of mental anguish, crying, worrying ,etc. and medication really helped her. In the meantime, I'd try to keep in mind that she is being cared for and is safe. I'd come up with words of comfort that will work for her, keeping in mind, that she likely will need to hear them over and over, since she will forget what you have told her. And, I'd try not to take it personally. If she were in your shoes, she'd do the same to keep her love one safe and protected.

With my LO I told her that I was checking with the doctor. There was rehab to be completed, therapy in process, forms to completed, etc. Sometimes, certain things work, but, there are some people who do not accept things and there may not be any magic words that help them feel better or dissuade their anxiety. Eventually, they may forgot to ask those questions though. Explaining things that require thought processes didn't really work with my LO. With dementia someone is not really capable of processing information, reasoning or using good judgment.

I think you know that you cannot indulge delusions or feed into them. Answering her calls is not going to help her and it's upsetting you. Answering her questions will not reorient her into her present reality. Get a white board and see if you writing out the answers to her questions helps. Example:

"Why am I here? You are living in a safe, clean space and you have everything that you need here right here at home."

Someone on another thread wrote about her whiteboard solution and I thought it was fantastic. I can't remember the thread or the poster but maybe someone else will.

You reassure her that you love her, you want what is best for her, that she cannot stay alone SAFELY ( really push the SAFETY stuff), and that the decision to place her in a facility was something that she knew from the start would happen, and did.  Then you join a support group for yourself, get support from your family, your church, and strap on your seat belt and be ready for the ride.  Maybe this facility isn't the right one for her, so look into another one.  I had to move my mother from the first one to a second one and she did much better at the second one.  She was at the first one for 5-6 weeks, and at the second one for nearly 2 years before I found another one that was smaller, more one-on-one with the residents.  She has been there now for more than a year.  All in all, I have moved her five times since I got her to start with--3 facilities, and two moves within two of the facilities because of her deterioration.  I have her at one that is a stairstep one which keeps her on campus, but as she deteriorates, she moves from one station to the next one that gives appropriate care that is needed for her stage of Alzheimer's that she is currently in.  She might move again.  Who knows?  I just try to hang on.  I've been doing this for more than 3 years now.  Good luck!