Sure your car wasn't leaking it? How did it get into antifreeze? Most causes are a direct result of the owners lack of respect for others rights to peace and quiet. Did you let it bark all the time? Did you not pick up its duties daily so no to cause offensive odors? I am a dog lover and have had dogs all my life and even I had thoughts of taking out the dog because of the lack of cooperation from the owner but could never do it cause it wasn't the animals fault. It was the owners fault for letting it do what caused a nuissance to the neighbors.
That is very sad. There is no sensible answer.
I am not really a dog person but killing a dog is going way too far.