My Mother thinks there are 2 of me. I don't know what to do or say?

My mother is 82 and recently diagnosed with vascular dementia.

She began periodically falling in 2012 / 2013 (2 times a year at most) and looking like she was having a seizure. Eyes rolling back, rigid body, gasping for air, then passing out for a few moments, coming around, vomiting. When she got to the hospital everything was normal. They would keep her a few hours, do the routine tests, and send her home. I kept asking each time if it cold be TIA (mini strokes) but was told no and neither was it a seizure. The Dr's attributed it to high blood sugar (she is diabetic for 25 years) and atrial fibrillation (she has had for 15 years).

In Sept 2014 she fell between two hotel beds, her head went sideways against the box spring on one of the beds and she broke her neck (thankfully not a vertebrae). They operated and put a pin in. Although a bit unsteady on her feet and range of motion on her neck is more limited, she is fine.

Then she started having falls again in Jan / Feb 2015 (3 in 1 month). She remained lucid and calm and said she tripped over the walker the first 2 times. Given the location of the walker and her eyesight, it seemed logical. The 3rd time she presented the seizure symptoms and vomiting again. Paramedics saw atrial fibrillation pattern on their monitors, took her to the hospital.

Same thing, everything presented normal when she arrived. They kept her over night,sent her home. A week later, we are back again in the ER for the same thing. This time the Dr.admittedher for almost 2 weeks, got the blood sugar under control, did CT scans, heart monitoring, blood tests, urine tests and were watching for another fall to see what the seizure looks like (which of course won't happen when you are in a hospital and waiting for it to happen). But again, they indicated there was nothing they could pin point but possible high blood sugar. Readjusted her medication a bit and sent her home.

Thankfully the falls have not happened again. Follow up CT scans since she left the hospital in Feb show her brain has become smaller and that she did appear to have had mini strokes. Her Dr. is attributing the vascular dementia to that. (my mother does perfect on any dementia test done in the Dr. office (except the short term memory part). But of course she would pass the test....that is the only focus needed in a very quiet room, not one bit like a home environment)

The dementia started back around early March, after she got out of the hospital. Just very slight confusion of thinking she lived in her childhood city. In May, she was displaying more signs of mild confusion when talking with me specifically. However, the Dr did not seem concerned and did not want to put her on another pill just yet (already on 10 in the morning). Did the UTI - fine.

Since July, she consistently thinks there are 2 of me. One is her daughter and I cannot figure out who the other one is in relation. We both have the same name. She will look right at me and say .. not you.. I want the other Sxxxx (meaning her daughter). She will stand at the top of the stairs and call for her daughter Sxxx to come up stairs when I am standing right next to her. She will make dinner for 3 of us (it is just myself and my mother in the home). Her daughter Sxxx is much younger I have concluded. 90% of the time I am not her daughter, but am the other Sxxx. She thinks my mother visits. She calls her "the other mother". There is no name she can give. But will often ask me if the other mother is coming shopping with us.

Everyone else she remembers perfectly. She talks with her niece on the phone every day. She talks to her brother everyday and knows everything perfectly. Both live in her childhood city.

Since August, she comes to my room and asks me where "Sam" is so she can wake him up, then goes to the spare bedroom to look. I have no idea who Sam may be and she cannot tell me. Sam was my dog that has been gone for over 10 years. Sam was her brother that passed away 20 years ago and had been married for 20 before that, so was not a constant in her life

I have a caretaker every day for 4 hours to help bathe, clean but mostly talk and keep my mother's brain active while I work.

It has gotten progressively worse the past couple weeks. Now 80% of the time she think she lives in her childhood home & city. She wants to invite her brother for dinner or drop something off to him (it is 2 hours away). But she knows where she is when he calls on the phone.

She functions fine in all other aspects of her life

I am at a loss as to why it is just me she is confused with. How do I respond when I am not the right Sxxx? When she asks me to get Sxxx to come in the room? She gets agitated and angry when I try to explain I am her daughter & there is only 1 Sxxx. She says everyone is fooling with her. I am tears most days as she can be quite hurtful with her words. I know it is her world at the time, and I try to go there with her, but it is hard.