How can we move someone with dementia if she does not want to go to a facility?

Is that private insurance you think will pay for an assisted living facility? Think again. She will have to pay unless she is indigent and on Medicaid. If she is lucid enough to sound "normal", then short of bodily taking her to a facility which she will pay for (with funds she gets from selling her house or savings), then she can stay put. If she truly has Alzheimer's dementia, she has to be in a locked facility which is more costly than an assisted living one. Get her doctor to verify which stage of dementia she is in, and then go from there. You have time.

Definitely a good idea to get your aunt's doctor on board. Send him a written note explaining the situation first - that worked really well for me.
However, much as the older generation respects their doctors, I've found that dad digs in his heels once he leaves the office! It's all "yes, doctor. I will, doctor." until we try to actually execute the 'doctor's orders'.

Depending on her stage of dementia, has she seen a geriatrician that has diagnosed her with dementia? or is this something you think? In any event, you could try to start with getting her into respite care and tell her it is a break for the daughters and caregivers, and from there she could just transition into a residential setting.

Purplesushi you are SO RIGHT. My mother who was falling frequently was refusing to consider a walker until the doctor told her she needed one. I kind of laughed when she said, "Oh, doctor...if you think I need one then ok." All I could think to myself was you've been my mother for 61 years but your doctor of less than 10 years has more sway. Regardless, though....it solved the problem for now, at least.

A formal declaration of incompetency is a last resort. If it's not plainly obvious, and it sounds like it wouldn't be, it can be arduous to get (as it should be) and can take awhile.
I'd meet with your aunt's children and formulate a 'plan of attack' – if your aunt is thrifty, appeal to that "you paid a lot of money for your long term care insurance and you could be one of the few people who actually get to take advantage of it and live for free!" If your aunt is able to be persuaded by a guilt trip, have her children make the appeal "I can't believe you won't even consider this for me. Knowing how I worry about you and how much I love you, how can you not even give this a chance. You are taking support away from your grandchildren - I can't provide for them as I could if you would use your insurance...). But, given that her resistance sounds 'toddler-like', you may be most successful by just laying down the law. Her kids could meet with her together (to show how serious they are) "We can no longer afford to support you. You must use your insurance. We are going to look at a community today."
Personally, even if I had money to burn, I'd be damned if I'd spend it on aides for someone who has long-term care insurance!
Her children need to confront her with reality or just move ahead and make the plans without her. It's hard being a parent to your parent!

Her daughters need to talk to her doctor, and have HIM tell her it's time to go to assisted living. I have sometimes found that the older generation takes the word of doctors as gospel and will listen to them before they'll listen to their own family. Just a thought.

I'll try this again. --- You need to get her declared incompetent. This process varies from state to state so check with your local office on aging and they can assist you. -- My mom has dementia too and for a very long time she sounded competent if you talked to her and people who didn't know her wondered why the family considered her incompetent. They'd say, "She seems fine." Don't go by that. I took her to a neuropsychologist and he tested her. He wrote a report that said that she definitely has dementia and Alzheimer's and detailed what she can and can't do. That's a legal document you can use to proceed to put your aunt in a facility that will properly care for her.

I pleased and pleaded to have my husband in a nursing home. Finally I gave up and then one day a VA emergency room doctor came and said to me "do you really want to take care of this old man? I said no, and that go the ball rolling. They transferred him to a nursing home. At that time he had vascular dementia, was tube feed and had urinary incontinence. So, find a nice doctor, explain the situation, and hope for things to happen on the next routine doctor appointment. Beware, they take them wherever they find an open spot. Mine was 37 miles from our home.

You may be well-served seeing an elder law attorney. The issue of competency needs to be resolved. It is difficult to "make" someone do something if they are legally competent - even if you disagree with their decisions and think they should do something else.

NO ONE wants to go to an assisted living facility. In the case with my dad, the doctor said that he could not live alone. My dad had every reason in the book and then some why it would not work. His arguments were exhausting. So we left the hospital and rehab and went to straight to assisted living. I already had his furniture moved in and his clothes in the closet. He pouted for about three weeks and that was tortuous for me, but he says now it is where he needs to be. My suggestion would be to get her doctor to talk to her, take her to the facility and let her look at it, and see if she will just "try it". Trust me, it is NOT an easy move for anyone involved, but sometimes we have to do what is best and safest.

Unless her daughters are willing to declare her incompetent, they are in a bind. I had to wait it out, until my mother fell and went to the hospital. Then, the doctor refused to let her go home.

Will she at least go to the AL and have a look?

Depending on the progression of her dementia, she might now be a candidate for AL, though.

Just because she sounds lucid to you doesn't mean she's competent. I can't tell you how many people thought nothing was wrong with my mother, yet when it came to competency, she couldn't remember the year she got married, her address or other essential details that help determine competency. If she is not competent, a guardian should be appointed for her.