I'm so sorry about your birds, this is just terrible. Please be very careful with these people. THey are absolutely capable of "upping the ante" to violence against you and your animals if you escalate the situation too far. I do think that you absolutely need to report the threats that were made to the police. But be cautious and realize that your life will get far worse if these people leave poison out for your dog, etc. If your suspicion is right, and these people are drug addicts or meth lab types, they are not in their right minds.
I am a golden retriever person, and I just can't imagine ever letting my sweet dogs roam free-- it is a recipe for them getting hit by a car, etc. etc etc! And I find most Jack Russells to be very, very obnoxious. But I think that it would be a terrible mistake to kill their dog. I think you would regret it deeply, since you have a dog yourself. If you feel you have to get rid of the dog a humane option would at least be to give it to a Jack Russell Rescue group, where it will be adopted by someone who is educated about the needs of the breed.
My gentle goldens occassionally take off after a rabbit or squirrel in our fenced yard-- ugh! I yell at them, but they are hard-wired for it. Luckily the animals are usually quicker than the dogs. I am sure your lab has chased squirrels and rabbits in the past, too. This poor neglected Jack Russell was bred to chase and kill small animals (in fact, they were largely bred by to have that drive by chicken owners who used them to chase and catch rats in coops). It needs guidance and training from its owners, which sadly it will not get. but that doesn't make it a vicious dog-- you have to remember it is their pet, just like your dog and chickens are your pets, despite the truly horrible behavior of the owners. I think if you kill this dog you will have done something very wrong, and will have given these awful people a very good reason to feel they can take revenge against your family. They might (and probably would, given what this woman said) kill your dog, perhaps in a horrifying way that could really scar your family (and especially your daughter). I remember a family I know finding their dog hung in their backyard after an ugly conflict with a neighbor about their pit bull. WHen you are dealing with nasty people you just have to be extremely careful, or the situation can get out of control. You also never know with drug addicts, they might even harm you. It just wouldn't be smart to confront them again if you can avoid doing so.
Remember that "an eye for an eye" philosophy just leaves both people blind.
It is easy for us, when we are wronged, to start to tell ourselves revenge is okay. It never is. I think you are doing the right thing in focusing your energy upon creating a really secure coop. But do let the police know what you are dealing with. If you have suspicions about drugs you could report that, too. But I think direct confrontation is not going to be helpful, and it might be really harmful for your family and pets.
