Is it permissible to take money from my aunt, who raised me and is afflicted with Alzheimer's, and who insists on giving me money to buy things for myself and my daughters, knowing that she doesn't care about anyone else but me and feels complete trust towards me?

Alzheimer's disease is like dementia, and it has two states: The first is when it severely afflicts a person, causing them to lose consciousness, in which case their ruling is that of an insane person; accountability is lifted from them, and their actions are not valid. As for the second, it is when this condition afflicts them for some time, and their ruling is that accountability is tied to them during the time their discernment returns, and it is lifted from them when they lose it. Therefore, gifts from your aunt are valid and permissible if they occurred during her time of discernment and awareness, but if they were given during a time of lack of discernment, then it is not permissible for you to accept them.