The dog's owner is responsible for the vet bills. No ifs, ands or buts. She is also responsible for the loss of your laying hens. Listen to what the investigating officer said about the length of time you owned them and the food invested. It may not matter to you, but what the dog owner needs is a wake-up call, and it sounds like her wallet may be the only think that will get her attention. Since you do not want the dog put down, may I suggest that you demand that the dog be rehomed to a responsible owner who will ensure that it is properly restrained. Chances are that you will not get this---but it may be a bargaining chip, and it may show her how serious you are.
I honestly doubt that her attorney said what she alleges about not being responsible for vet bills or that the cost you asked for being too high. She was making excuses and trying to look/sound more righteous; and attempting to limit her liability, or at least convince you of it. Or if the lawyer did say it, he/she believed that your birds wandered into the dog's yard, not that the dog dug under a fence to get into the birds pen on THEIR owner's property.