Should I tell my mother, who has Alzheimer's, we are going on vacation?

I don't think I'd discuss in any detail. However, I would get the person who will be taking care of her to start coming in while you leave the house. That will ease her in to having someone else there.

Res19hud: Perhaps there is no real need to tell your mother that YOU are going on vacation, assuming all the while that she'll be cared for.

If you acre caring for her in your home and she will be going elsewhere - tell her.

If she lives in a memory care unit - tell the administration where to find you.

No. You should not tell her. I don't know how advanced she is in her Alzheimer's if it's early stages or further progressed.
I'm assuming that you or someone else has arranged the appropriate caregiving services for her while you are away. Of course if she's in managed care, that's not necessary.
Iameli in the comments is right. Your mother stressing herself out and working herself up into hysterics because you won't be right there could be a real possibility.
Depending on whether or not she is still high-functioning, a staged "fall" or health "crisis" the day you're supposed to leave for vacation can also be a possibility. So you miss your flight or train or whatever and spend the day in the ER for absolutely nothing.
Don't tell her you're going in vacation. Don't even call. Have whoever is taking care of her call you only if there's an emergency.

I agree with everyone here but just wanted to ad that she won’t remember what you told her anyway.

I agree that if she has good care then don’t tell her. We had to tell my MIL because she lived alone, but her worries were all about what if I need something or what if I get sick (she had 5 adult grandkids she could call). So if she’s taken care of and won’t notice you being gone I would not subject her to needless stress.

Enjoy your vacation!!

A vacation? What’s that?

what's a vacation?

The hardest thing for me to remember is a “caregiver has a lonely life/no collaboration with LO”. When I chat with mom and share too much, she misunderstands and stresses.

SO, a year ago, my husband and I had commitments that took us away from mom for about 5 months. All I told her was that I was working on a project but I would be calling her every day on my break. My mom got used to my calls (I used Alexa Echo Show so I could drop in and she could see me). I have done this since for family visits of 3 weeks and all is good. Mom is content and safe and doesn’t think about me not being away because she doesn’t know. I also have Amazon deliver her underwear, sleep sock, palazzo pants, lotions, shampoo, shoes, Ensure, straws, -pretty much anything she needs. She lives in AL but the service depends on the staffing and the inclination of the individual staff so I got her a private caregiver who works 4 hours a day 1-5 p.m. which works great for her.

Bottom line: absolutely do not tell her you are not nearby. One time mom asked me where I was and I said “in the middle of helping Cliff -my husband”. That worked. I made a joke that helping him means I get to stand and hold things above my head while he looks for the screw driver! She laughs and all is good.

Why would you tell her?

Do you live with her or she you? Will she wake up and a stranger be in your place? If that is the case I still wouldn’t tell her but I would have the caregiver coming in ahead of time for them to become acquainted. It seems unkind to tell her if it would cause her to stress.
Have a nice vacation.

Assuming she will be cared for 24/7 while you are gone, I see no point in bringing up the vacation at all. In my experience the caregiver/s and my mother have a smoother time if I don't tell her about vacations or any other times I'm out of town at all. Telling my mom only causes anxiety and panic and endless pacing.

Where is she living? If she's in a facility or at her home with 24/7 care, no, don't tell her.