My mother with dementia has started obsessing over the neighbors. How do I stop these obsessions?

I agree with Margaret, but it concerns me that Mom is allowed to wander without supervision and be out long enough that her “stalking” might creep out the neighbors. I have pretty good control of my faculties (most of them anyway) but I can be prone to tripping and falling.

Supervising and in a way, controlling Mom has to be up to you. If she is to remain at home, she cannot be allowed to wander off. Today, she goes next door, then later down the street and after that, maybe around the corner. People with dementia can be very sneaky. My mom was. They have no filters and don’t realize they need a coat to go out in winter or that it’s not safe to cross a busy street. They wait until your back is turned and off they go.

Going door to door and explaining Mom’s issues is ok, but she really needs supervision before something traumatic happens.

It would be sensible to talk to the neighbors who are affected, and perhaps discuss with these children's mother what she thinks is the best way to handle it. That might include letting you know that your mother has turned up and needs to be collected, or talking with the children about how to react. I am sure that the mother will want to know if there is any danger, because that would be situation that needs to be controlled ASAP. However many children have always known that 'there is a silly old lady down the road', and have coped OK with it. It sounds as though this 'obsession' isn't necessarily bad for your mother, it really is a case of making sure that other people can cope with it.

Since there are children involved I believe you need to put an end to this, have you told the doctor? You also mention sneaking out of the house so I assume someone is there, you/they need to get an alarm for the door to make sure she doesn't go out unsupervised.