buy a game camera. gather evidence, and call the authorities. dont kill the dog. not it's fault the owner is a dirtbag.
you can get a decent game cam for around $150.
HEY! i just bought a device called a SCARECROW. it attaches to my garden hose...everytime something trips the motion sensor..a sprinkler (rain bird style) sends a high pressure spray.."chish chish chish!" you can set the angle it sprays. it would cover alot of your yard.
i got it for deer and it is working GREAT!! sprayed me a couple of times
need a pic? cost me $50 from amazon.