As I try understand my grandmother's behavior I see that she manifests many cognitive and psychological sleights of hand. She will insist that truth is the most important thing to her, and then outright lie; or she will insist on being treated like an adult but then not want to handle responsibility. It is easy to get up caught up in sophisticated theories to explain this behavior, but in the case of dementia the psychological complex seems to be different.
The model which has best served me is Robert Sapolsky's lectures on mammal and human aggression. From his lectures I interpret the situation as one in which my grandmother desperately wants to keep the alpha female position as a householder, and will relegate my responsibilities to the kitchen and shopping. Any incursion or suggestion outside this realm and she will claim I "want to call the shots" or that I want to be the boss.
This makes my job here a thousand times more difficult, because I must uphold the illusion that my grandmother is in charge of house, but then she will be overwhelmed by her responsibilities, she cannot admit to her incapacity because she's afraid I will take over and this will cascade her stress and make her more hostile. She conceals her incapacity by putting blame on me, and where she admits fault she apologizes profusely.
I doubt it will be possible to ever gain the position of the householder, which would make both of our lives much easier. It is her home, and her environment will always prompt her to dominate. Still, by conceding to all of my grandmother's demands I'm way down on her illusion of hierarchy. At this time, when she makes a demand, I stare at her a couple of seconds with a dominant stance, and then say "Ok grandma".
She has an operation on Friday and is already stressed to the limit, she almost growls when she speaks. I'm focused on reducing stress, not gaining status at this time. Our relationship is a process.