Linda,
I think you need to take pictures of her rental house to document it being empty. Lots of people are not aware that MANY homeowners insurance companies frown upon homes being empty for more than 60 days. It makes the insurance policy void. Many agents who sell you the policy turn a blind eye to it but the home office and claims department will have a conniption fit when they find out. I would try and find out which insurance company she has and inform them she has had the house empty to be rented for XXXX time period. They can and will cancel her policy. Even if the insurance company doesn't cancel her, I am sure they will raise her premium due to increased liability.
I would also really research the history of her property. You can go to the building permit department and pull records from her property. Most people do not pull all necessary permits for home renovations. You can also find out lots of information from the county accessors office from the comfort of your computer.
I think you need to let them know loud and clear that you are willing to work with them on resolving neighborly issues but you will not be bullied and you have no problem stooping to their level. I would also spend a couple of hundred bucks speaking to an attorney to see what your options are. You might be in a more powerful position than you think. I would also try and get your story on the news, local paper, and youtube. Have you tried googling your neighbors name? You can go online into county court records. All civil and criminal cases can be researched. Civil cases are usually a matter of public record and sometimes, so are criminal cases. Right now, you are perceived as the inconsiderate neighbor with the loud roosters but you might find out your neighbor has a few skeletons in her closet that will help you out. She might be the neighborhood pain in the a** and there is always someone willing to tell you the neighborhood gossip.
But make sure you have your behind covered. I know you have reduced your rooster population and I know that helps. But can you get a cock box to prevent the remaining roosters from crowing at night or at the break of dawn? Have you asked your other neighbors if they can hear your roosters at night?
Hope this helps!