The first thing the family needs to do is to understand what kind of controlled environment your Mom needs. I assume she is the one with Alzheimer's.
For an Alzheime'rs patient, the closeness to the family is important. At this point, it seems now she is close to you either way. The elder needs a familiar environment because she is forgetting a lot. Your Dad seems to think the current house is not safe. She needs to stay in the familiar environment unless the house is too old or in a real bad neighborhood or does not meet the need for the elders with dementia. More lands does not really help the elder with dementia since it will be strange to her.
What she needs is a controlled environment so there will be 24 hours watch to make sure she does not get lost and etc. She could even go to the neighbors for help so familiar friends/neighbors are a plus also.
However if the current house has something wrong (too old or too many stairs for the elderly,) then the family may want to find a smaller condo or move your parents to the independent living home where there are health care support like an assisted living home. Many facilities have the combination of independent living, assisted living for dementia, and skilled care nursing home.
It depends on what factor your Dad is looking at. Maybe he is looking at the wrong factors. A new house is good if it is controlled so that she would not get lost. This has nothing to do with safer neighborhood or not; she needs to be watched so she does not get lost. If it is in a remote area, it is worse for her to get lost.
Usually the person with dementia is incompetent to decide where is safer or better for her. The family should set up meetings to discuss the true need for an elder with dementia or Alzheimer's.