How do you talk to your mother who thinks she should live with you?

You answered your own question. For your own physical and mental health you cannot have her living with you.
Don't let anyone tell you otherwise. Believe me when I say your mother would not be happy anywhere she moved. She would not be happy living with you either.
She praises your cousins who had their mothers living with them because in senior culture it's like a higher status when someone's adult kids move them in because it looks like the senior is the family's top priority and that they're still in charge of the family.
I've worked with elderly people for almost 25 years. In homecare and for AL communities. I remember the daily conversations in the dining room with the old biddies who would get judgmental about a resident if they had adult kids who were not at their beck and call and willing to do everything for them. That they must have been a "bad person" or parent. Or the talk in the bingo halls when there are seniors with adult kids who won't take them in. They are very judgmental. This could very well be why your mother wants to live with you.
Whatever the reason, do not move her in. It will be the worst for you both and your child. Stay strong and don't' get talked into it.

Why are you afraid of upsetting her with a frank conversation? She doesn't seem concerned about upsetting you with her assumptions.

My mother and I always laughed about the fact that WE COULD NEVER LIVE UNDER ONE ROOF, so sure enough, when she became too disabled to live alone, I INSISTED THAT SHE COME AND LIVE WITH ME.

Usher in 9 months of Hell.

When we finally placed her she loved 5 1/2 years of happiness.

When you talk, start the conversation by saying “No, Mom, it’s NOT a good idea for us to live together”.

My mom and I were very different as well. Everything from colors (important to me) to what kinds of entertainment we enjoyed. I lived with her for 4 years, then had to find other solutions for her care: home care and eventually assisted living. It was best for both of us and she was not even difficult to talk to, though she did pull the silent treatment occasionally when not getting her own way. Then, at assisted living, I was her daughter again instead of her caregiver and we had fun visiting, even at the window during covid lockdowns. I still advocated for her, including all financial and medical needs. However you handle this issue, it will be difficult, but living together will be the most difficult, since she is already hard to communicate with. Just answer her praises of your cousins and her hating where she lives with the question of where she would like to live and when she would like to start the research to make that plan. And it won't be living with you.

Don’t do it if you don’t want to..because then you’ll resent the whole thing. Will she be happy anywhere? Or she just wants company being miserable…& to join her in misery? If you think you can do it short term from 6mos - 1yr…that can easily grow into 5 years or more. Certainly, if you know you don’t want to do it now…you’ll want to do it even less later. Hugs 🤗

I get the impression from your question that you are confusing "how do I get her to agree with me and like it" with "how do I get her to not live with me". Preventing her from living with you is easy: you say no. No adult has the right to move into another adults home. Just legally/factually speaking all you have to do is NOT move her into your house.

How do you get her to agree that she shouldn't live with you? You can't. You can't control what another person thinks. You can't make her agree with or like your decision. You only control yourself. She doesn't like it? Tough, for both of you. She doesn't have to like it and you don't have to do anything to fix it. She wants to keep asking? You tell her to stop and if she won't you end the call or visit.

You may not feel safe and in control, because of all the emotional manipulation, but you 100 percent are. It's your home, all you do is don't move her in.

just Keep saying no. In whatever way you are comfortable. I was nicer about it in the beginning and now I’m more blunt. If she is so enamored with the cousins maybe she can go live with them.

It is always best not to tippy-toe around these issues. Failure to meet them in a kindly and open manner will cause all kinds of trauma and anxiety for you both. Sit Mom down and it goes something like this:
"Mom, I have heard you more than a few times talk about Aunt June moving in with Irma and the kids, or your friend moving into her daughter's home. I think I we should discuss this now so that we can make plans how to proceed in the future. I have to tell you that I will never live with you nor have you move it; it isn't an option for me, and isn't open to argument or discussion. I love you, but I don't want to live with you. So I wonder if you would like to discuss now options or plans we can make to keep you nearby, and to help you and keep you safe. We should discuss what papers you are created (advance directive, DPOA, will) and what your assets are; we should look at your files if you would like help with them in future, and at your accounts. We should perhaps even explore what is available in our area before a move is necessary in future. I would like to tell you I will always be here to help you indecision, always willing to explore these things with you, discuss your wishes for end of life care, what you would want and what you wouldn't. Once we settle these things, hopefully far in our future, we can relax and know we are about as prepared as we can be, given that 'Man plans and God laughs'".
That's about all you can do. You can't control HER reaction, just be certain you don't A) argue B) react in anger. Smile, say you thought it might benefit the two of you to discuss this, and will always remain open and ready to do it.
My parents always wanted to stay four steps ahead of what might come, so we discussed things way earlier than we had to. I was a nurse and saw a lot, and knew it was a good idea.
Best of luck to you both.

We have lived in the same house for 25 years. Among other things, one of the reasons we stayed here (being youngish when we bought it) is that the house is NOT elder-friendly. This has already come in handy once where we dodged the elder-moving-in issue because particular elder could barely navigate this house at the time we moved here 25 years ago. Even SHE could see that it wasn't going to get easier with time and additional frailties and she really could not safely move in to age in place here with me.

There was one short moment in time where we did consider moving out of this house and into another home. Elder was ALL about us doing so. Oh yes... she perked right up. She even took a family member on a drive by of the house we were looking at and gleefully exclaimed that there was an extra bedroom (assumption: extra bedroom was for her).

We made no further strides towards buying that house with the "extra" bedroom. No way. We did pass on that house, but it was worth it to have our fears confirmed: elder WAS planning to move in with us, but realized she could not do so unless we moved to someplace more user-friendly for HER. It was nice not to have to officially say no to her, but wow. Just wow. The nerve of assuming that our property is somehow hers as well. And it wouldn't just be living space. She would expect full-on caregiving and maid/butler service even for things she could do herself. No, no, and no.

Of course, the day will come when WE will not be able to stay here either because we will be too elderly/frail to safely live here ourselves. But I'd rather know that and have the chance to plan for it as opposed to having an elder decide on a dime that he/she will move in.

Your mother, like mine always did, is using passive/aggressive manipulation techniques to cow you into agreeing to take her in to live with you. She has a skewed view of how perfect life will be in YOUR house, 5 minutes away from HER house, where life will be Grand, regardless of the fact that life is NOT grand NOW, that you two don't get along, that there will be nothing for her to DO in your house, and that the oil & water relationship will go even further south than it already has! She doesn't want to hear the truth b/c then her fantasy will be blown to smithereens and she'll have to face reality. Can't have that happen, not with a passive/aggressive personality who wants THEIR way or NO way at all. Not to mention, were you to take her in, she'd SEE for herself that life in your house is even worse than life was in her house, and then it would be Your Fault you 'forced her' to go live with you in the FIRST PLACE! See how passive/aggressive minds work? Like a broken & twisted clock that's running on a dead battery!

Here's a good article on the subject: https://www.excelatlife.com/articles/crazy-makers.htm

So, when she's ranting on about The Cousins who are So Perfect, my response would be: Gee, Isn't It Unfortunate To Have ME as Your Daughter? What a Raw Deal You Got in Life, huh Mom? That normally shuts them down for a short while, until the next rant feels warranted in their mind.

Come up with a standard line about why it's impossible for mother to come live with you: your house is too small, you don't have room, you are a psychotic prostitute who trolls the streets nightly for tricks and cannot have ANYONE knowing your secrets, whatever. It won't matter your excuse to her, she just wants to hear Okay Mom, Sure, Come Live With Me, No Problem! Anything else is just Blah Blah Blah Blah Blah.

You're the Bad Guy, so just own it, as I have my whole life. I was the only child too, who could do no RIGHT in my mother's eyes. It was what it was, so I owned it. I quit trying to make excuses for why I wasn't all she wanted me to be. I just wasn't, and that was okay too. She lived in Assisted Living (Memory Care at the end) and wanted to live with me & my DH which was impossible. She'd get very angry with me towards the end of her life when her dementia was very advanced & I could no longer 'reason' with her at ALL. So I just told her I loved her, and I would go see her frequently, and bring her small gifts and snacks, etc. There was nothing more I COULD do, honestly, but watch her decline and then finally pass away last month. I spent many hours with her at the end of her life, so I hope she knew I was there. I was always there for her, just not in the way she WANTED me to be. Sad but true.

I wish you peace, my friend, b/c you won't get it from the person you want it from: your mother. She will withhold it from you b/c you're not giving her what SHE wants, and that's something you don't really have the power TO give her (I believe), and that's self-love. Mothers like ours don't possess that, and feel like they can get it from others; that if they come live with us, they'll feel better about themselves or find that missing 'something' they haven't been able to find their whole lives. But they don't, b/c that missing something comes from WITHIN. That's what I believe, and why I wish you peace, b/c you deserve it.