WTBH, stay clear of them. I was also in an abusive relationship, which your next door neighbor is in right now. I never went thru what you are going thru though, but sometimes I think that if this happened to me, and I was being abused, that would have just listened to whatever my H was telling me at the time, and try to isolate myself from you and your children.
I'm not a vocal person, so I don't think I would do what she is doing, but some abused people are vocal, and they take it out on someone else, because she knows she can't say anything to her H.
Calling the cops on your ex, could have threatened her ex. She might have gotten an earful, and she couldn't give it back to him, so she gave it to you.
Advice, I really have none, except to keep your side of the street clean.
Resolution? I have no idea !!!!!!!
Why did your ex show up at your house? Pls, note that I am not blaming you for this.