My mother has alzheimers. How go I handle her constant questions about "going home? "

Depends on context. Often difficult depending upon the stage of ad..Frequently patients placed in ltcf or alfs will pose this question frequently-best to be honest but reassure them this is home & that you will see her often & she will be taken care of.Repetitions will often result in success but is late stages the best strategy is to divert their attention to other more pleasant issues or defer to a futur date.
Alzheimers questions. The best general reference is mace and rabbins excellent handbook for families: the thirty six hour day. This provides many helpful strategies to deal with the changing family dynamics in this disease. Alzheimer's patients can learn. It takes simplification and many, patient, repetitions, over and over. It helps to involve the patient in decisions and keep notes for them to reread later.
Repetitive questions. Every person with ad has different needs and responds to behavioral interactions differently. For those that always ask when are they going home (and they are home), reassurance and reminders of the home they live in may be enough . Some may never believe they are home and may even believe that you are not her daughter(you are an imposter); these challengin behaviors need help of a skilled doctor.