I never had an AARP policy, and in fact, canceled the membership - more for political reasons than anything else.
One thing to keep in mind is that the Medicare plans lettered A through F, G, and whatever all give the same coverage. That is, all plans A are the same as any other and all plans F are the same as any other plan F. Don't know if that helps any at all, or not.
As for someone being able to live with, and care for an Alzheimer's patient, I know a few who have done it. If anyone tries it, they should definately plan on professional help that can come in and provide a few hours relief from time to time.