I beg you to take a deep breath and pray for calm when you go to talk to them, because you never know just how crazy some people can be.
I have a friend who was in a similar situation a couple of years ago, and her furbaby ended up dying from poisoning! She could never prove anything, but she knew it was them! Being neighbors might have made access to the pup easier because they could watch their daily routine.
Two years and a skin baby later, she still morns her "first born" and the mention of her Barbarella brings tears to her eyes. She ended up moving a continent away!
It just breaks my heart.
I don't mean to be such a downer, but an a**hole is an a**hole, and it sounds like your neighbors really take the cake in that department!!!