I feel we are talking about different diseases here. When your mother becomes irritable for the length of as wait, an Alzhiemer's patient won't do that. They can't remember where they were going and why. Leaving her in the car is not a good idea, btw. An Alzhiemer's patient would get up and leave.
My mother had Alzhiemers and for a while she was combative with others but that didn't last long. She will forget who you are and claim you are something you are not. My mother thought I was a "train lady" trying to schmooze her husband.
The best advice I can give to a person caring for an Alzhiemer's patient is to "enter their world" and agree with what they say. My mother went into Alzhiemer's care late in the game. She thought she was in a Country Club and when she had a lucid moment, she wanted to leave. We told her the cab was coming and she settled into doing something else. Give them things to do like folding laundry. When they are "done" take the basket in another room, mess up the towels and repeat the task.
I used to take my mother for rides and to the store. She thought I was her mother then and wanted to bring her ceramic pekinese with us all the time She thought it was a real dog and pet continually. It was very soothing to her. When we entered the store, I assume my role of mother and reminded her not to touch anything. She held my hand and we walked. Very slowly and talked about anything that entered her head.
My father did not fare well with my mother. He kept telling her she was wrong about things and it agitated her more. When she swept the carpet with a broom he became upset because she wasn't using the vacuum. He never got it straight that if she isn't bothering anyone or doing something dangerous, let her be. Tell her she is doing a good job and thank her. Enter her world.
The time will come when she can no longer communicate. That is the loneliest and saddest part of the disease...for both of you. While she is still communicative, please remind her how much you love her. There will come a time when you no longer can and it will break your heart.