Mom lives with me and gets sad, cries wanting to go live back in her house. How should I handle this?

These are all signs of her dementia. My mom always wanted to go home as well, the home of her youth! I's encourage you to stop correcting her and go with the flow. Go to the alzheimer's website, they have some wonderful info. The 'good' part of dementia, is the ease with which you can distract the person. Agree and change the subject.

She may confuse you because you are her daughter but you are also her caregiver. What exactly does she say and when does she say it? Were you two close before she move in with you? Maybe she misses doing things with you...

Some additional details might be helpful. How old is your mother, and how long has she been with you in your home? What does she say about your other half? Does she make comments regarding the mysterious "other sibling," describing her as more or less a separate individual with unique personality traits or an imaginary "history"; or is this just based on what she thinks she sees in the present time? Perhaps a visit to her optometrist might be in order; or if she's making up stuff, an evaluation by a neurologist.