My mother's (92) doctor has said that she should be in an adult care facility! How do you get a person to agree to go?

Do you have the legal authority to make this decision for her? Are you her PoA or legal guardian? If her dementia is that bad, she won't be legally able to sign the intake and billing paperwork. Does she have the funds to pay for AL or MC? I have to ask these questions because the guidance given to you here depends on your answers, especially if she never cooperates but needs to be moved for her own protection. It may turn out that APS moves to acquire guardianship and at that point they call all the shots and won't be waiting around for her to agree to anything. Your family wont be involved in any management or control of her medical issues or financial assets.

Actually you don’t know how she will react when admitted to a facility unless she’s already been in one.
She is living with a progressively failing brain, and it’s unlikely that detailed discussion will make much of an impression on her.
Bearing in mind that the doctor’s recommendation is based on her needs for safety and structured care and management, tell her the day you plan for her to move that you and she will make a visit to see a friend of yours. NO mention of her staying.
When you arrive, tell her you want to introduce her to your friend, and as soon as she is surrounded by the caregivers, quietly leave.
Ask the social service worker in charge to let you know when you should return for a visit, and follow her suggestions.
If she has her own phone and is still able to use it, answer one call in the morning and one at night, and unless the facility advises, no more.
Her job, and YOURS, is to help her learn to rely on her caregivers, and break her hold on family members.
If her behavior is still inappropriate in her new home, she may need an exam by a trained geriatric psychiatric specialist who can prescribe calming medication if necessary.
If you begin to receive complaints about her conduct, ask the facility to recommend the psychiatric specialist whom they use (this problem is observed fairly often).
This is often the hardest part of the extended care experience. Once she is somewhat settled, you will be able to enjoy visiting, and she will too.

Best of luck.

'The Doctor says so' actually works for some.. yes really.. it depends on personality.

The scale may be from "whatever you think is best dear. Where do I sign" to "well.... OK" after 12+ conversations to "Pigs will fly! Ain't nobody making me do ANYTHING I don't want to do! Ever!!!"

So first, identify your mission. Know your enemy. Prepare for battle. Grab your hat. Your steel helmet of common sense.

Mother is in battle mode - fighting the good fight against old age, frailty & loss of her independence.

The trick is if SHE decides to concede, she will still be IN CONTROL.

Many folk will hopefully write in with he steps on HOW to get this done.

My take today is battle prep. Take heart, it CAN be done.