Hospital will not diagnose stroke. Any advice?

Are you new to using the internet by any chance? You need to remove you and your mother's full name and city from your profile asap. You're asking to have your identity stolen.

Are you aware that there can be complete aphasia due NOT to a stroke? (What Is Aphasia? — Types, Causes and Treatment (nih.gov) ).
There are many reasons for what you describe. Stroke cannot always be diagnosed even with an MRI UNLESS it is a hemorrhagic stroke, which always shows on CT scan. That is more rare than the common strokes.
I am really so sorry that you haven't a hard and fast "diagnosis" that you can understand, but that doesn't always happen, and you have some fine hospitals on board here.
Can you tell me why, in your own mind, you wish to have this diagnosis? Is there some difference it can make for you?
I do know with my own brother it was never a case of a hard and fast diagnosis we could hang our hats on. It was "probable" early Lewy's Dementia diagnosed by symptoms he had. It was "possible" benign calcified tumor and then location given and the "guess" that it was likely a decade old, and affecting his sense of smell and balance, but, hey then, it could be the Lewy's. It is always hard not to have a diagnosis.
The longer your Mom remains without recovery the less chance for her to recover. In most strokes what you get back fastest (2 weeks or so) is what you get back most easily. What remains is hard rehab work, and sometimes simply unattainable.
You are currently in the most dread room in the house, and that is the "waiting room". It is so difficult to wait, and uncertainty is awful. I am so very sorry and wish you much luck. Hope you will update us.

Similar situation I had with my Dad: he got a phone call, talked normal, wrote down gibberish, and had no idea what he had written down. Then he was putting on his boots to leave but didn't know where he was going. Sent him to emerg via ambulance. He called me 2 hours later upset they hadn't bothered with him for "16 hours!" and said he was going to leave. I told him no, STAY THERE! We called the hospital to get them to make him stay, but the nurse said "his body, his choice!" and let him leave. He fell in the parking lot and never walked again. He did have cancer, but the day before was walking and talking normally. He died 9 months later (from the cancer) and just had no strength in his legs ever again.
They blamed it on everything but stroke, no actual diagnosis, maybe this, maybe that, but nope, he for sure did not have a stroke. I think they were covering their own butts, because they didn't recognize the signs of a stroke and let him leave by himself.

I agree there is something wrong but I am sure MRIs and CT scans have been done. The only other thing you may try is an Eye Doctor, Opthamologist. My Mother had lost her Peripheral vision in her left eye. The doctor did a test with lights to determine if the loss of vision was a stroke or her Dementia, it was Dementia.

You mention high sodium

"But too much sodium in the diet can lead to high blood pressure, heart disease, and stroke. It can also cause calcium losses, some of which may be pulled from bone. Most Americans consume at least 1.5 teaspoons of salt per day, or about 3400 mg of sodium, which contains far more than our bodies need."

"Sodium blood test results that are higher than normal may be a sign of a condition, such as: Dehydration, which may be caused by not drinking enough, diarrhea, or certain medicines called diuretics (water pills) A disorder of the adrenal glands. A kidney disease.Jun 2, 2022"

Mini strokes are strokes.

Where did you get your medical degree that makes your opinion superior to multiple trained doctors?

Sounds like you've just been googling symptoms (and copying and pasting the results into your thread, judging by all the random capitalized parts) and jumping to conclusions.

Unless you're a doctor, listen to the doctors, especially after hearing second opinions.

There are lots of reasons why someone might have those symptoms, and stroke is just one of them. My aunt had similar issues and it turned out she had a surplus of calcium in her blood due to as-yet undiagnosed multiple myeloma. She had at least two episodes of that, but of course, it was diagnosed relatively quickly with blood tests and remedied until it happened again.

I think you should stop doing the diagnosing if you aren't a medical professional and let the experts handle things.

BerthaErvin, welcome to the forum. So sorry to read of the medical issues with your Mom, she is still young by today's standards.

You have been to 3 hospitals, thus what was the diagnosis of your Mom's condition? Curious, with the fall, I wonder if your Mom had head trauma? Sometimes with a head trauma, it can cause dysarthria.