How can we make my grandmother accept elite private care?

No matter how you try to sell this idea to her, calling it elite, will not make a difference.

Is she competent? If so, she has the legal right to decide where she wants to live. It is YOU that is going to establish boundaries that you will stick to.

You've picked the wrong stumbling block.

Your biggest issue is identifying whose decision this is. Your profile states that your grandmother is only 74, but that she has had a stroke? and is living with dementia?

If her dementia is advanced, she may no longer be able to make key decisions for herself in which case the family can act for her, first applying if necessary for guardianship (unless somebody already has power of attorney for her).

If your grandmother is still able to make decisions for herself, then she must plan her own care with support from the family. What you can do is withdraw the option of her care being provided in your home: she can decide where she lives, but she can't decide that she's going to live in another person's house without that person's agreement. She thus has to make her plans choosing from the options which actually do exist, which for example might be the facility the family is considering, together with two or three others for her to compare it with.

There is one other thing you may long for but cannot hope to achieve. You say you want her to understand the reasons for moving her to residential care, which amounts to wanting your grandmother to be happy and gracious about moving out of your care and into a facility. But who can be happy at the thought of being more than their family can handle? Be realistic in your expectations of her.

No, not familiar with that particular facility but I have toured Assisted Living facilities and they are lovely. I would encourage placement for her.

Have you toured this place? Are you satisfied with what they offer? Can you look up reviews? Can you speak to any of the residents or family members of residents?

Best wishes to you.