My mum keeps asking me to come over and take her to her home across the road from her friend although I tell her she is there.

Try to redirect your mom's attention. As GardenArtist suggested tell your mom that you'll take her tomorrow or that the friend isn't home right now and you'll have to take her another time. Then try to get your mom interested in something else such as another topic of conversation or a tv program.

Does this happen more in the evening than during the day? If so, perhaps you could tell her that she can start some minimal packing and you'll be over tomorrow to take her home, as it's just too late in the evening to make the move.

Andi, sometimes when our elders say they want to go home, they mean the house where they grew up. Could it be your Mum is talking about a grade school or high school friend who had lived across the street some place else?