You keep claiming that they are top tier escape artists like nothing can be done and it absolves her from keeping them on her property, but it just means that your sister needs to build something better to hold them. Honestly she can pay for a lawyer and fight this, but her money is probably better spent building a cage that can actually hold the dogs and coming up with settlement terms with the neighbours (which will probably include the cage anyway). I would add cameras to the property and possibly trackers to the dogs to provide future information.
I know that she doesn’t believe that the dogs have done this, but as others have said it doesn’t really sound like coyotes either, and as you have pointed out multiple times the dogs are escape artists. She could possibly win the case, but her dogs are still an issue.