Ah the age old debate...my neighbors are inconsiderate about their animals & it's impacting me in my property....what to do, what to do???
I would 100% guaranteed NOT sacrifice one of my ANYTHING, ESPECIALLY not one of my dear girls, for the satisfaction of catching the offending animal, making sure that it was covered---even with 1 drop---of blood for the Animal Control Officer to see.
Dear OP, you are venting and not solving the problem. If you have already done so, good.
I haven't read thru all posts yet. I did read that you weren't rasking for advice. Plowing ahead anyway, if yourn neighborwon't fix the issue, it falls squarely on you. Interaction 1 was an unspoken 'shot across the bow.' Interaction 2 told you it was on. Dig a hole & bring it.