Hi there,
I feel for you.
My mum has Levy Body Dementia, which differs slightly from "normal" alzheimers. (it includes some degree of hallucinations and psychosis in addition the the disorientation and memory loss of alzheimers, coupled with some Parkinsons treats) She lives in a nursing home now, as my dad is disabled and in a wheelchair, and unable to care for her.
I have made a "memory album" for her. It is basically a selection of important photos, in chronological order. A few photos from her youth, her wedding photo, baby photos and family photos including my sister. Photos of me as a baby, photos of our family as me and my sister grew up. Photos of my mums family. And photos of my sisters daughter, and my children, etc. They are glued into an album with descriptive captions under. This means that anybody can pick up the album and talk to my mum about the photos. They can say "Oh look, this is you on your wedding day, what a nice dress you have!" "This is you and your oldest daughter." and the idea is that her memory of her family and her life can be kept alive for her by anybody, not just me. She loves her album.
I agree that a parent with alzheimers is still the same person within. But they are also a new person in their own right, and this must also be recognized as the time spent with them now is very much on their terms, and it is important to both follow their lead, and also to a degree bring them into OUR reality. Although, I think my mum prefers to stay in hers, most of the time, and I let her.
I am getting to know her all over. She is still the same lovely woman as she has always been, but her life as it is now, is different from the one she shared with us.
She now has a baby doll. He has the same name as my youngest son, whom she loves very much, and to her it is a real baby. My mum is living the life of a young single mum, whose husband have left her, and she is having a work placement in an institution. She worries about her babys eating, finding babysitters, what her parents (dead of course) are up to, where her siblings are, etc. I play along with this, so as not to upset her. I dont lie to her, but I dont correct her either. If she asks me how her mum is, I say I havent seen her in a while, but I assume she is fine. The conversation then moves on. If I were to tell her that her parents are dead, it will be bereavement all over again.
Most of the time she does not know who I am. She recognizes me, and she loves me, but as SHE is a young woman, she does not connect that I am her daughter, as I am too grown up for that, seeing as she is a young woman now.
This means that when we meet up, I let her think I am her sister. It does not matter who I am, as long as we have a good time together.
If I call her, I tell her "hey mum, it is Quintess, your youngest daughter, how are you today?" And then I talk about my life, my issues, and she will very often be able to follow the conversation and it becomes clear that she remembers things I have told her previously, and it is possible to "keep" her in my sphere for a little. She may after a while start talking about her babies, and I let her. Then I can steer the conversation back to me, or real life for a bit, and she is with me some more.
It is only natural for your relationship with a demented parent to move on, and change. Try to think of it as getting to know a new person who has very similar personal characteristics to your mum. It will get easier!