I'm so sorry about your losses and that your son will have to face this heartbreak. I'd report it and I'll explain why.
This animal is not only a proven livestock killer, but it's possible he has attacked before. After all, he broke through a barrier. What if he goes for your son? You? You have been reasonable, God bless you, and if this dog is going to live next door, you are not safe. Wait until the Easter week-end is over if you must and see what the neighbors do for your loss, but report it anyway. Tell them you have done it. In fact you should compose a letter and register it to them in the mail.
There used to be a vicious dog on the property below ours and over time he killed some pets (not proveable) then moved up to attack little girls on the public road that goes past that house. One girl was hospitalized and is badly scarred on the face and neck. This is what it took for everyone to get serious. Yet if the dog had chased a cow the farmers would have hunted him down and killed him immediately.
Also, if you can, do a little checking. Sometimes when people own a vicious pet they will relocate. It's possible this dog has attacked before and it would be useful to know.