are they going on your property? If they are? can get a game camera which will give proof, call animal control.
Dont kill thier dog, that will open a can of worms.
You are repairing the fence? check your laws and see resposibility is it 50/50? If you keep fixing fence you may be able to charge them if you were to go that direction with this.If you fix the fence and cost you money save the reciepts.
reciepts, game camera pictures, call animal control.
I skimmed thru maybe missed something.
Good luck
my 2 cents