I really do not think moving her will phase her much since she does not remember much. Just having someone there to comfort her and be nearby is what is definitely best for her. She may not know who you are but she does know that someone is there for her consistently.
When my Grandfather had AZ, he did not remember anything that he did at that time but remembered things about the Korean War and other various activities done 30 - 40 years before. He also did remember faces but of course did not recognize who they were or why they were there. But, he did say a few times that he was glad to see someone again if they came back to visit him from day to day. So, it does have an impact on them if they see you on a regular basis.
There may be others with some suggestions here also, I think as your Mom does not recognise anyone it may be easier,she will be nearer to you anyway so that is a good thing, just from my gut feeling it would be good for someone to be with her she is comfortable with on the journey also with her when she gets there to her new surroundings,Good luck I hope the move goes well let us know how she is doing.