Should we just ALWAYS agree?

Has she been diagnosed with anything specific yet?
If, after you talk to her doctor----and DO talk to her doctor---the doc says he's done some basic Q&A testing with your mom and he thinks she's not suffering from dementia symptoms, then call her out on her behavior.
She may be depressed as she is recognizing that something isn't quite right. That's understandable. My In-laws ended up both being put on Zoloft at their gerontologist suggestion under the heading of "it will help with your feelings and memory issues". Folks of their generation think you're broken if you're depressed.
However, you and your family do not deserve to walk on eggshells every time she opens her mouth. Just as you said, it is affecting everyone. Can you see you and your husband living with this behavior until she passes away? It sounds like she's otherwise in very good health. For all your kindness, you are being repaid with hatred. She may be hating herself and not you, but it has to be worked out, one way or another.
Do NOT always agree (as you asked). It will end up eating you alive.
I am sorry you're going through this. It sounds like you and your family love one another very much and your Mom, too. It sounds like she's not herself, and you'll have to step in and get her some help.

I'm honestly shocked by how many of these replies sound fairly critical and unsympathetic to OP and her family. They are doing the best they can and she came here because she needed to talk and be heard: not lectured. I think many of us can understand where you are with your mom. The fact is that caregiving can and does destroy some families, leaving them divided and fractured. And as the child of the person being cared for, you feel guilty that your spouse and children have to shoulder this burden with you as well. But don't carry it alone. They love you and will help you while you help your mother. I suggest seeking a helper or aide a few days a week for your sanity alone. I have one and when she is here, go to my room and decompress, don't think about my mother or her care, read, write, shower or nap. But listen, you are human. You will get frustrated, get angry, get your feelings hurt. You are not a machine. And anyone that lectures you differently happens to be having a decent day where they feel superior. Talk to them on one of the crappy days when life as a caregiver is a true struggle. When your mom is behaving this way, don't engage. If she is feeling frustrated and angry already, you don't want to escalate her behavior. We want her calm and peaceful. A polite agreement is truly the way to go. It will keep her placated and help you keep your sanity. The anger she is displaying is indeed due to the fact that portions of her brain are shrinking and dying. If she was already negative to begin this, you are in for a challenge beyond measure as the disease progresses. But try your best not to take it in and not take it personally or it will destroy you. Don't let that happen because you are too valuable for that. You matter. I heard every word you said and felt the emotion behind your frustration. I know how hard it is. I know you love your mom. And I know you are doing your best. Hang in there.

I know exactly how you feel. I live in the UK, and used to work in administration in an over-65's mental health unit. So I knew all the 'best practice" stuff.
But when it came to dealing with my own mum, all the good intentions can sometimes go out of the window.
I have learnt that it's no good correcting her when mum says something I know is completely untrue, and have to bite my tongue at times.
It's hard, especially as she has always had a bit of a nasty tongue and turn of speech.

My husband, 77 with Lewy Body Dementia, was doing this and it progressed into outbursts so vitrious that they were triggering my PTSD. Using his son as a mediator I sat down with him and told him that I will no longer tolerate these outbursts and if he does it one more time he was going to a facility.
That conversation got some things out on the table. He was frustrated b/c he has lost his freedom to drive and feels trapped. I work on more outings and his he has kept his temper and those constant rude responses under control. My threat stands. If he flies into a temper one more time, he’s going to a facility.
We have to set healthy limits as caregivers. I cared for both parents and my brother simultaneously and my husband joined the list. I am not Wonder Woman.
Even with dementia, my husband has not forgotten to behave since I drew the line.

My mom was a pain with always being so touchy, sarcastic, thinking we were ganging up on her and generally being a real cranky and disagreeable human. I never even considered that she might be depressed or have anxiety. It got so bad one Christmas that after she left, I promised she would never darken my door again. But I called her one day and she started up again and I let her have it - all my frustration, how her behavior is affecting the family, how no one will want to spend any time with her if she keeps up this behavior. I kept assuring her that I loved her but hated her behavior. She went to the doctor herself after that and was put on medication - I call it her happy pill - I'm not sure what it is, but it has completely changed her mood. She is back to the person I always remembered.

Remember, your mom is not so old or feeble that she can't be talked to like a person. Maybe your mom is tired of being "agreed" with. Maybe causing drama is entertainment. Maybe she just needs to be stood up to.

Of course, if she is suffering from dementia, I don't recommend this at all.

Just my two cents.

This may be far out....but... (because I have a bad reaction when I feel this way)...I wonder if she feels that you are being condescending toward her.
You are going to great lengths trying to be "nice." I hate it when people do that to me, because I feel that they are just trying to placate me without acting on MY concerns.
Especially if she has been in a position of authority in her career, she might have been suspicious of subordinates who tried that with her. So, if she's cold or wants more cat food or whatever, what does she want you to do about it? Ask her. Then respond appropriately: Pointing at thermometer, "It's 78 in here. That's what we like. You want warmer, go outside or get a sweater." "Oh, thanks, I'll put cat food on the list." Why argue about that?
I am not dismissing your concern about her cognitive abilities, and they need to be addressed by her doctor. I'm just suggesting that you try to react with less seemingly placating behavior.

You mention her good intentions to see an attorney. Get recommendations or do some research and be ready to make an appointment the next time she brings it up. Immediately. If it's after hours, make a big note on the refrigerator to call first thing in the morning, then do it. Give her an appointment card, write it on the calendar. If she starts "you're pushing me," just tell her she already has the appointment, so she may as well go see what they suggest--she doesn't have to agree with them or do anything if she doesn't want to. Then, go with her and keep your mouth shut when the attorney tells her what she needs. If you are asked for your opinion, say "It sounds like good advice to me, but it's really up to you, Mom." The attorney will tell her what happens if she doesn't have DPOA, etc., then let her decide. Don't second guess her decision because you think she's not competent to make the right one. If she's not competent to make the right decision, it's too late anyway, right?
As others have mentioned, you need a break. Why not visit your daughter's campus for Homecoming or just a fun weekend? Ask Mom what she wants to do while you're away. Staying by herself in YOUR house not being an option you are going to accept because, "I couldn't enjoy it if I was worried if you are OK." Have two or 3 options for her: in-home help, stay at a facility, whatever. She pays for it, because you can't be at her side 24/7/365; you'll be crazy.

You could be talking about my Papa here. If he misses his medicine, he’s stupid. Or he’ll argue about something trivial. I think it’s because he has no control left in his life and he’s angry about that. He hates that his doctor has told him if he falls he has to go back to the nursing home. He hates that he can’t see to do anything around the house anymore. He hates that he can’t drive so we have to take him. He just hates the fact that he’s not in control of his life anymore and there’s nothing to be done about it.

I have two words for you : Teepa Snow! She has video on Youtube. WATCH THEM! She does break it down on how to deal with your loved one when they had Alz/Dem. You can't argue with her, because you will lose. She is also "Showtiming" you; tell you things and you correcting or agreeing with her ("I know"). No she doesn't know, because she can't rationalize anymore. I left her brain ten minutes ago, you are late. LOL! I have been going thru this for four years; at this point I just say Okay Mom. You can't let it get to you; she has no control in what she is saying. (Easier said than done) If I had a dollar for every time my MIL was doing that to me I would have been a MILLIONAIRE! Teepa Snow watch all of those little ten minute videos; I think there are 16. WORTH IT!

OMG. I thought you were writing about MY mother. Virtually identical situation but at least she doesn't live with me. I feel your frustration. It does make you feel that you are walking on eggshells even when you think you're saying something innocuous.

I try to just humor her. Frequently I just take the abuse. Not sure I have a lot of suggestions to offer, but wanted you to know that you are not alone.

That's unfortunate that she is refusing to sign Healthcare POA and Durable POA. It will put you in a bad situation, when the time comes for your to make decisions and handle her affairs, because without those documents, you'll likely be hampered. I might consult with my own Elder Law attorney, NOT the one she is consulting with, but, a different one and get info on what you can expect when the time comes. You can also get some tips from around on this site, from others who have had to file for Guardianship.

I'd also explore what types of care that she might be entitled to. It's not for the children of the person to pay. They pay with their own income or assets, and if they don't have enough, they may qualify for state or federal assistance with the costs. There are normally, some forms of in home assistance too.