Total firetruckin bullshit!

Get yourself a couple of security/ video cameras that can record audio, and record as much as you can of this type activity

The suggestion of capturing the dog is a good one

Waste no time in researching the laws in your area related to loose animals, trespassing, noise ordinances, how vigorously enforced they are, and waste NOT time in calling in legitimate complaints. Noise, trash, trespassing, loose animals

Are they renting or buying? If they are renting, raise hell with the owner. THREATEN to sue the owner for "maintaining a public nuisance." Even if you cannot be perfectly serious, it will get the owner's attention, and he/ she might "take a look" at what they have brought to your door.