Yes, Pete, the desire to "go home" is often a desire to find somewhere safe and escape the confusion of the dementia and the home they are seeking is often a childhood home..
In this case, though, I think it is more likely to be Capgras syndrome (where they think that the real place has been changed for a fake) or Reduplicative Paramnesia. Both of these things are caused by damage to the brain, including dementia.
This site gives a brilliant explanation of Reduplicative Paramnesia
http://sites.psu.edu/alexaugustpassion/2016/04/13/reduplicative-paramnesia/
In this case, though, I think it is more likely to be Capgras syndrome (where they think that the real place has been changed for a fake) or Reduplicative Paramnesia. Both of these things are caused by damage to the brain, including dementia.
This site gives a brilliant explanation of Reduplicative Paramnesia
http://sites.psu.edu/alexaugustpassion/2016/04/13/reduplicative-paramnesia/