Ron, as you are in the States, I would like to mention one other topic. It's not related to what you asked about, but it's a piece of information I didn't have, when I needed it. I hope you will please forgive any distress or upset this causes. Then we can go back to talking about how to get your mother to the neurologist!
What I want to tell you and all the other American posters is, should it ever come to it, don't be afraid of the Geriatric Psychiatry Unit, also called GeriPsych, also called the (Senior) Behavioral Health Unit, depending on the hospital. I know that they get a lot of bad press, especially in the States, and especially on another Alzheimer's discussion forum that shall remain nameless. I think everybody thinks it's still the 1960s and Nurse Rached and all that. I'd like to say, that was NOT my experience.
When the UK posters talk about having someone sectioned, it's basically what we in the States would call, having someone committed (also a scary term, with negative connotations). I think the more up to date terminology is an "involuntary admission" or something like that; again, it depends on the facility.
This generally means a secure (locked) unit in a hospital for as long as it takes, but usually at least a few days, to figure out what is going on with the person. It's not exclusively for dementia, of course, it could be any number of issues, physical, neurological, medication problems, you name it.
In my case, that was what had to happen to get my mother diagnosed, and into the care facility she needed.
I hope it won't come to that with your mother, and I don't wish to alarm you unnecessarily. It's just that it's not something that is widely discussed or understood in our health system. If I'd known in advance, not to be afraid and how helpful it would be, it would have been less stressful when the ER doctor (at another hospital where my mother was taken after a crisis) brought it up to me. I am fairly experienced at navigating the US health care system but had NO IDEA about this, and of course at a stressful moment, it's hard to cope.
Should your mom ever have to go to the ER for an injury or accident or other health problem, and it's clear she either needs further assessment and/or can't return to her home immediately, it's something the medical staff may bring up.
So I will get off my soapbox, and I am sorry to hijack your thread.
I hope you're able to get your mother to the neurologist, get a diagnosis, and start to get some help. My mother's primary care doctor sold this idea to her (of the neurological assessment) as "a specialist I want you to see so you will sleep better," as that was the only problem my mother would admit to, but he was an exemplary primary care physician. I know they're not all that helpful.
If you will bear with me, and again apologies for anything upsetting, there are some other issues to consider, such as legal and financial issues, and also getting support for you and your mother.
Depending on where you live, there may be some support groups and possibly other resources in your area. If you go to the homepage for the US Alzheimer's Association, you should be able to find a link for listings in your area, by state and county, for support groups. Failing that, call them, and they will help you figure it out.
Also depending on your area, you may have a state, county, and/or city wide organization to help with senior citizen services. It's called various things, like the Council on Aging, or the Committee for Older Adults, Eldercare, or Senior Services. If you Google "[name of your city] and senior services," you should get a hit. If that doesn't work, try the same thing with your county of residence, or state, if it's a smaller one. If that still doesn't work, the local office of the Alzheimer's Association may be able to help. And if that still doesn't work, any local social services organization, or nursing homes, should know and be able to give you their name.
I have attended various workshops, lectures, and support groups run by my local Senior Services organization and the Alzheimer's Society. In addition, some nursing homes and even hospitals, or health systems, offer these types of classes and support. It has been a wealth of information and a huge help.
On the paperwork and legal front, if you don't have Power of Attorney, you want to get that taken care of ASAP. You want a very good elder law attorney for this. If you can't get a recommendation through friends and family, you can try the local Bar Association, or the local Senior Services office. This is very important. I had a lot of heart-stopping stressful moments before I got the Power of Attorney sorted out, although to be fair, I didn't have much trouble getting the doctors and hospitals to work with me (it helps that I'm an only child and my mother has no other relatives). However, doing anything financial without one, is basically impossible.
The elder law attorney will be able to guide you about other issues and paperwork, such as a will, durable Power of Attorney for Health Care (a living will), longer term financial issues (the dreaded spend down to Medicaid), and so forth. But get that PoA in place, first thing. Again, a good attorney will work with you, and not make you bring your mother to an appointment she doesn't want to attend, but instead will come to you.
I feel sure I've overwhelmed you, with a lot of information you didn't ask for, but on the off chance it could help you or some other American reader, I'm including it. It's stressful to have to figure out all this stuff on your own, as if the dementia weren't enough to deal with!
Again, please don't hesitate to ask questions, and very best wishes to you.