mutilated bunny rabbit in my fenced in yard?!?!

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Ok last weekend was hell.. but there is one thing I cannot figure out.. In my backyard that is fenced and the doors padlocked there was a mutilated dead rabbit! I'm an animal lover so this broke my heart.. ill try to explain without going into too much detail since its really gross.. After we had gotten home after being gone a few hours, we let my dogs out, and it had been less than 5 minutes and then when we checked one dog staring at the rabbit scared and the other one licked it but that is all.. neither dogs have ever hurt other animals or anything and when I looked at the wounds it was like it was cut surgically NOT a dog bite.. it was the shape of a dog mouth, but then it would have been jagged and torn not like perfect! It was cut this way on both sides.. There used to be a rabbit my lab/boxer would chase to the hole of the fence but the bunny was far from that hole and blood headed to the fence door.. neither dog even the one that licked it wanted to touch it any further.. the one that licked it did not lick the wound but licked the clean area.. there was no pool of blood underneath the rabbit.. the dog that liked to chase the rabbit that would get into our yard isn't the type to hurt it but was just chasing it out of fun. I seriously do not think my dogs did it and why would the blood be far away from where the rabbit comes instead of the door? I'm scared to think of the possibilities almost.. I'm afraid someone jumped our fence and did this in my yard.. the neighbor kids have jumped the fence when we had taken some of their puppies, so I know they know how to jump it with ease.. the lack of blood except the streak makes me think it may have already been dead or just killed and then put in our yard to scare us.. We do not have a good relationship with our neighbors because we had turned them in for animal abuse and neglect and one of their dogs got taken away.. they know its us because we confronted them a few times because the dog was causing damage to our shared fence.. we recently refinanced, which meant we had an appraiser out, and I'm wondering if they thought we were going to move and then decided against it or something.. I caught the neighbors trying to feed or catch my dogs even though they were in my fenced yard, and so I'm wondering if they were going to get revenge on my dogs for theirs.. which my dogs wouldn't go near them, and my dogs love everyone! What do you think? Is there some serial killer in the making in my neighborhood? I'm positive the dogs didn't do it, since they had NO blood on them, and we never found the missing pieces of the rabbit.. The whole thing makes me want to cry since I love animals so much and its really bothering me that if it was a person that they went into my yard and did this then what is next? any ideas on this? I hope this wasn't too gruesome, but I tried to not let it be but the situation kind of made me have to give a few details.