What can I do to make her understand she cannot live alone?

Your mother will not consider help other than you as long as you continue to be all the help. Harsh as it may sound it will take you backing off and refusing to jump at her demands for her to see that she cannot cope on her own. And please reconsider believing that moving a demanding person with many needs into your home is a good idea, it would likely ruin your home and relationships. Go back to work, leave mom to it, tell her your income is needed, and she needs to find other help. Don’t continue a pattern of being all the help, it’s not sustainable without great cost to your health and well being. When mom sees she’s unable to make it, hire in home help for her or arrange her move to assisted living. Feel no guilt, it’s okay to be sad that it can’t be different or better, but guilt is for those who’ve done something wrong and you haven’t, you’ve simply been placed in an impossibly hard place and need another plan

Stop.
Just stop doing it all.

Obviously not just 'cold turkey' but as safe as possible.

This is my 3 step plan as advised by a Social Worker for my LO - living alone but definately NOT independantly.

1. ADVISE
Have a good chat.
Make it CLEAR what you can do going forward & won't you can't. If you are going back to work, tell her this.

Advice her if she wishes to 'age in place' she can! Having the right help/support will allow her to age in place longer.

2. LET HER DECIDE
Help her make a list of what she needs help with. Then help her source all the required services eg dog walker, house cleaner, grocery deliveries, meal service, personal care support aide for showers of required. Include transport: Would taxi/uber be safe? Maybe you will keep doing this? Or a paid personal aide drive her?
Mother decides on the services she needs, can afford, what to trial etc.
(Umm.. you may even find the list so long that an entire village of people would be needed to keep her boat afloat. Let that sink in 🤔. For both of you.)

3. CONSEQUENCES
The consequences are hers.

Fired your dog walker?
Pooch may have to live elsewhere.
Refused meal delivery but can no longer cook? Eat toast.
Refused to let the shower aide in? Stay unwashed & undressed that day.

Then you circle back to 1, 2,3 as often as you need.

Tough Love.

You are enabling her. As long as you prop her up she has the appearance of independent living. Back off. Let her fail so to speak. She might realize she needs more care or she ends up in the ER and you tell them that she lives alone and it is an unsafe discharge. Go back to work. You can't afford to jeopardize your own future to appease your mom's stubbornness.

As long as you jump when she orders she will continue to not cooperate.

You need to stop allowing your mother to take advantage of you. Her choice is between hiring more help or moving to a living situation that provides the level of help she needs.
You do not need to be one of her choices. You do not even need a list of justifications for that decision. You need to stop being he Go To Option.

Be very clear about what the plan is. Keep telling her you are returning to work(even if its just PRN) and she will have caregivers. Do not move her in with you! Not sure what her age or health is. Get groceries delivered to her door. I used "Mom's Meals" for my mother which is a better quality of food and can be catered to health needs like low sodium. Can your mom use a microwave? Do as much online as you can including ordering house supplies. Get her prescriptions delivered and I requested child proof caps to keep mom out of the pills.
As for the caregivers start out slowly like two days a week or half days & increase as needed. My mom enjoyed a split shift 10-2 & then 5-9p.m. She napped in between.
I changed mom's insurance so she could have a visiting physician. We also use a mobile lab and a mobile Imaging company.
Good luck & do not let her demand your life away.

By doing everything for her, you are allowing your mother to 'refuse' to do this, that & the other thing. Once she's on her own and SEES what is actually required to live 'independently', she'll realize in short order that she's not capable of doing so. Of course, dementia may prevent such a realization from setting in.........but time will tell, ONLY once you stop enabling her. Dementia causes an elder to become self-centered to the point where nothing & nobody else exists except THEM. They lose all sense of empathy as they become focused only on their own desires 24/7. You're going to have to wait for a crisis to happen that forces mother into managed care from the hospital or rehab. Either that, or you use your POA to place her in a Memory Care ALF against her wishes IF she's been diagnosed with dementia and/or deemed incompetent due to that diagnosis.

If you don't stop doing everything for her, your entire life will be consumed with mother's needs in short order, and it still won't be enough. The reality is, she needs 24/7 care by a team of caregivers now, but the dementia prevents her from seeing the logic of the matter. I hate dementia and dealt with it for years with my mother who died in Feb at 95. She lived in Memory Care AL, thank God, and it was difficult enough for me as it was with her in managed care. I can't tell you how much I STILL had to do with her in MC.

To answer your question & summarize this comment, there is nothing you can do to make your mother understand she cannot live alone. Leave her alone to fend for herself entirely and MAYBE she'll see she needs to move into AL, maybe. It's likely a crisis has to happen in order to force her into managed care, though, that's how it works with the vast majority of elders (including my own parents who were forced into AL after dad fell & broke his hip after refusing to use a walker).

I suggest you read this 33 page booklet (a free download) which has THE best information ever about managing dementia and what to expect with an elder who's been diagnosed with it. It'll give you better insight into how your mom thinks nowadays.

Understanding the Dementia Experience, by Jennifer Ghent-Fuller 
https://www.smashwords.com/books/view/210580

Jennifer is a nurse who worked for many years as an educator and counsellor for people with dementia and their families, as well as others in caring roles. She addresses the emotional and grief issues in the contexts in which they arise for families living with dementia.

The full copy of her book is available here:
https://www.amazon.com/Thoughtful-Dementia-Care-Understanding-Experience/dp/B09WN439CC/ref=sr_1_2?crid=2E7WWE9X5UFXR&keywords=jennifer+ghent+fuller+books&qid=1657468364&sprefix=jennifer+ghent%2Caps%2C631&sr=8-2


Wishing you the best of luck with a very difficult situation.

It sounds like you keep trying to make her happy and satisfied which is never going to happen because that issue is where she gets her power. Everyone wants power. You need to get over your own need for approval and remember that her need to be demanding is not more important that your own marriage and general life. If you make choices that you think will satisfy your mom no one will be happy, not even her. So there are hard choices to be made and you must be guided by your brain not your guilt. If guilt rules you will be controlled by those who are the most demanding, not those who are deserving of your love and care. It won’t be easy because it involves transforming your own instincts to please in the name of peace. But that is a fallacy. It is not fair to ask the rest of your family to sacrifice for someone who is so difficult. Your mom isn’t accustomed to having to be adaptable so she is or will be angry. But there are worse things.

Anger and intimidation. Intimidation and anger. This is what bullies do. Of course you're not going to move in with her! That should be stated loud and clear every day and multiple times. She needs to go to a care facility, however you can accomplish that. You and your family deserve your life back and she's beyond reasoning, so do whatever you need to do. I wish you luck.

Stop enabling her by doing things for her. My mom was the same, we refused to move in more than 3 hours away. We did make sure she had food, the lawn mowed, ,bills paid.... She insisted she was living in the house til she died. She almost got her wish. We found her on a Friday afternoon on the floor and dehydrated. We pumped her full of fluids, loaded her in the car and took her to our house. SHE WAS HORRIBLE at my house screaming for the police because I was hitting her....( I was not). When she proclaimed she wanted to live anyplace but my house, she got her wish and is currently in a tiny, 12 bed assisted group home. Of course she hates it there...... Her failure to make a plan does not mean I am the fall back. Mom was never close to us or loving. My siblings will have not part of her.