What is the best way to get my mother to leave and move in with my sister?

At this point since is totally dependent on everyone else, this is not a choice situation, she must move.

Either she goes with your sister or she goes to AL or MC.

Move her things to your sisters, have your sister pick her up for lunch and she takes her home with her.

We have moved our step-mother twice, we don't tell her, we go there on the day, move her, she has FTD, we get her set up, spend time with her, and leave. By the time we leave she doesn't even know that she has been moved.

My brother & I make all the decisions for her, we have no choice, she is not capable of making rational decisions herself.

Sorry, I didn't see the Alz/Dementia part. That would change my response :
Just arrange everything you need to.

Mom has rights to be taken care of, as befits her age & condition. However, she does not have the right to insist that care is provided by a particular person (even her adult child). Or that she live under your roof.

A caregiver always gets to say when, how much & how long.

Let mom know you are moving on X date and that the house will be sold. She will need to be out by X date as you will no longer own the home so neither one of you can live there anymore, legally. Since she has ALZ/dementia, she probably won't understand what it all means, however. But you can pack up her things and ask her where she'd like you to take them? To your sister's home? Or perhaps she would prefer to move into a nursing home instead? Maybe if you give her that choice, she will choose your sister's home.

If she doesn't choose your sister's home willingly, I'd still pack up all her things and on the day of the move, I'd either call a car service to transport her to the new house or take her there yourself. I mean, there are no other choices here; you're moving, she's not coming, so off to daughter #2's house you go mom. You are under no obligation to take her with you. But if she cannot live alone due to ALZ/dementia, then you have to bring her somewhere else where she will be taken care of, like your sister's home or an ALF or nursing home to live. If she has no funds to self pay in managed care, you'd have to apply for Medicaid to fund her stay there.

Good luck!

Well I don't know about legal rights.. but socially. Sure. Sell up. Move. Mom will be forced out.

A friend's parents did this. Sold the house. Moved to the country. Helped set up & pay first month rent for apartments for their young adult children.

Kinda the same.

What's Mom's plan? A sit-in protest? In the empty house? Will all food & furniture gone? Water & electricity turned off?

If Mom is saying she will refuse to leave, why so?
Fear of change?
A manipulation bluff?
Or actual cognitive problem understanding?

Reassure her she will be ok.
That it will happen.
Keep the details simple.

How stubborn could she be?