Just a little comment - and I'm only on page 3 with my reading - I don't think it's necessary to keep a dog like that away from other animals for the rest of its life; I think it's necessary to re-train it. A handler works with a dog like that with standard dog training and then increases exposure to different sorts of animals under controlled conditions (leash at first, etc) with the handler present and teaching expected behaviour. That way you can teach just about any dog to do the expected thing when with the handler. When not working with the handler, the dog is restrained like all dogs should be. Just because a dog is displaying an undesirable behaviour doesn't mean it's necessarily like that forever.
The dog is two and a half, would have been easier at a younger age. That is why I believe the dog would be best off with a rescue, a good, reliable rescue. Then it could be assessed by knowledgeable people who would be in a much better position to determine if the dog can be rehabbed.
HarleyWood, if you can afford it you could take her a trainer (check all references) to evaluate the dog. Maybe a trainer could help you enough to keep your dog. I hope you have been considering all the advise that has been offered. You are in a horrible situation. I'm sure you love your dog, but please understand the danger that she is in and could pose to other animals. One complaint could also cost your parents their homeowners insurance. I know it's not fair, but almost every insurance group lists dangerous dogs as a reason to deny insurance, or add dearly to the price.
A dog that has been allowed to kill animals without any restrictions is danger to people in a very scary way. They do not have to have ever shown aggression to humans to have a running, squealing toddler set off it's prey drive. I'm not stating for a fact that your dog would do that, but I certainly would not be wiling to take that chance.
Your dog NEEDS a professional, either with you or in a rescue. And she needs to be contained until a professional says otherwise.