When we had a problem with a neighbor’s loose large dogs coming onto our property, we tried dealing with it neighbor to neighbor for a long time. When I found the dogs chasing our horses, I told my husband that next time I’m calling Animal Control, which I did (it was just a day or two later).
I managed to contain one dog and, when AC came out, the officer told me 1) it never works to try to handle these situations directly with the neighbor, instead, call AC first, and 2) the presence of the dog on my property proved that the dog had been loose and chasing livestock. Here, chasing livestock is a big deal, so I second telling AC that you have livestock. That particular dog was euthanized.
Some time later, the other large dog belonging to that neighbor, which had also chased our horses (but which I hadn’t caught) kept my husband at bay when he was walking our Shih Tzu around the neighborhood. Husband called to tell me – I went outside and saw him standing down the street, holding our dog in his arms. When the loose dog noticed me, it came onto our property, running aggressively towards me to the point that I retreated into our house, at which time it went back to the street. I went outside again, and snapped a few photos of the dog in the street, and then of it on our property (as it came back to chase me again). I called AC, and the officer who came out told me that each photo was worth a $500 fine to the owner (so thousands of dollars in total). That dog has never been loose again. I second the recommendation to take photos to prove that the dog is on your property. Hit the owners in their wallet.
Recently, there were two large, aggressive dogs loose in our neighborhood, chasing and attacking cars (did obvious damage to one’s bumper). Multiple people called AC, and I myself spoke to one officer who came out. I stressed that we and our next door neighbor have horses, that the people across the street have an assortment of poultry (and that I’d seen the dogs in that yard), and that there are older people in our neighborhood who can’t walk safely down the street with those dogs loose. Haven’t seen them since. With this latest incident, the first person who called was informed that AC needed more than one report. I suggest trying to encourage your other neighbors to also pick up the phone and call AC, which will assist in making a paper trail.