If the mother is suffering from Alzheimers and dementia to the point that she is putting things in the neighbor's yard, then the family needs to intervene. She could end up harming herself or someone else. And regardless of her mental state, she does not have the right to trespass on his property and he has the absolute right to call the police when someone trespasses on his property. What happens if she is on his property and gets hurt? The family would most likely sue. His protection against such a suit is having the trespassing documented. The way to do that is to file a police report. He has a right to protect himself and his property.