I recommend this book. Brenda Negri was a member here, I think she had an illness , she disappeared. I’m dumbfounded by the price of this book, on Amazon it was $192. I found a used one for $25. I have a copy and while I don’t agree with everything she said, there is much to be gleaned from her years of experience.
Brenda's book is still available for $27.00 on Amazon. (I saw the ad for $192 which is ridiculous) It is based on the trans-humance way of shepherding. This is leading out the flock to grazing and returning at night or staying out in open grazing with the sheep and dogs. For this type of sheepherding you need a larger number of dogs that coexist and work as a pack. No fences are involved because this type of sheep raising takes place on open rangeland. Many older Basques in Bakersfield, CA, still use this type of grazing in the mountains on forestry leased land. This is also the type of grazing
@SageHill does with her herding/guardian dogs.
Brenda's book is
very good as it focuses on learning to read your dogs, understanding the tones of their barking, understanding the ways LGDs work that often puzzle us until we understand what they are doing and why, and how to train them using their own natural reactions to livestock and dangers. I enjoyed it and learned a lot. She also discusses her use of several different breeds of LGDs and how they work in different ways. Brenda is battling some severe health problems. She is also working on another book about her experiences working on large ranches, etc.
With regard to your dog and her escalating aggression, I would seriously consider putting her down. If you do not choose to do this, she should be confined in a kennel run on concrete with a top from which she cannot escape. Since fences won't hold her (Pyrs are escape artists) a kennel with top and bottom is your only choice.
Allowing an aggressive dog to run loose is asking for a serious problem to occur when she encounters someone and bites them. Since you know that she is becoming more aggressive means that you have no defense if she attacks someone. At that point the authorities will put her down for you, and you will be responsible for any damage to people, animals, etc. that she causes.
Since she has been with you 5 years and was previously OK with your sister and the animals she was used to protect, putting her down would be the best solution. She might have a brain tumor or other illness which could be causing this behavior but since you can't afford a vet visit and any necessary surgery or medications for whatever is causing this new dangerous behavior the best solution is to painlessly euthanize her before she injures someone severely.
As animal owners we all need to remember that we not only have a responsibility to our animals to provide them with a healthy life and proper care, but to face the inevitable when it comes. This means putting an animal down painlessly when they are in uncurable pain, illness, or become a danger to others and/or themselves. It sounds like your dog has reached that point.