Neighbour Abusive

Hi, Day before yesterday, a woman, who lives in opposite apartment to ours (not in the same building, but our windows are opposite to each other) called my wife to the window and asked her if someone had asked us about her. My wife was confused as she only had interaction with her 1 or 2 times prior to this. We don't know anything about her. So my wife said "I don't know anything about that coz i don't even know you and why would anyone ask me about you". She said that person was high profile and told that please tell her if someone asked about her. My wife replied the same that she does'nt even know her name. That conversation was over. Then yesterday she again called my wife to the window and told her that she knows the person had talked to my wife and that my wife was talking to him late at nights and they were having an affair or something. making ridiculous claims. My wife and i were both confused as to what this lady was saying. She just said that my wife was having an affair with a person we dont even know and that person was someone important to her. Then she went on to say she had made a police complaint but did not mention for what. That the police would do their job and all. At this time i asked my wife to just stop talking to her, coz she was making weird claims and we were so confused as to why she was doing so. We are on rent here and its been 8-9 months. My wife was upset and went to our next door neighbours to ask about her as they have been living here for years. They said that she is mentally unstable. So we said Ok, we will not have any interaction with her at all. But since today morning she started abusing verbally, not directly but indirectly saying that whoever is doing this will face the police. The police are in my pockets and they will know wat i can do. I was not bothered coz we did not do anything and we dont' know what she is saying. So then she said that my kids should die and everything not directly but coming to the window and shouting indirectly. This has caused me concern for my kids. They are just 4 years and 2 years old. Why would someone say something like this for little kids. Please advise.