First of all, a dog never kills out of jealousy. If a dog kills another dog, especially puppies, there must be another reason. Unfortunately, there can be different reasons and we cannot diagnose your dog over the internet.
If someone (a dog or human) feels pain every day, they get grumpy. It's not unusual for dogs who are constantly in pain to become very aggressive. They are frustrated by being in pain all the time and they don't want other dogs to cause more pain (by certain interactions and movements).
It's impossible for me to say where she hurts, it could be her spine or neck, her legs, a bad tooth or any of her internal organs. If her behavior changed in recent times (like limping, playing or eating less), it could give you a hint of where the pain is situated.
It sounds like you don't control which of your dogs breed with whom. That means sister and brother could have babies, or mother and son. This is called Inbreeding and can have different effects on the dogs.
Specifically, inbreeding has been found to decrease fertility as a direct result of increasing homozygosity of deleterious recessive alleles. Fetuses produced by inbreeding also face a greater risk of spontaneous abortions due to inherent complications in development. [...] Viable inbred offspring are also likely to be inflicted with physical deformities and genetically inherited diseases. Studies have confirmed an increase in several genetic disorders due to inbreeding such as blindness, hearing loss, neonatal diabetes, limb malformations, disorders of sex development, Schizophrenia and several others.
Inbreeding affects not only the body, but also the brain of animals. It could be that your dog is schizophrenic or has another mental illness that makes her kill the puppies. If that's the case, it cannot be cured.
The only way to avoid inbreeding is to desex all of your female dogs so they cannot have babies anymore or to separate the male dogs from those female dogs that are not desexed.
Another possibility is that your dog is malnourished. She has enough food and isn't starving, but the food lacks certain components (like a certain mineral or vitamin) that she needs but doesn't get enough of.
Malnourishment can manifest in changes of behavior, but usually a dog starts eating things that are not food or obsessing about food.
To diagnose malnourishment, a vet needs to take a blood sample and analyze it in a lab. Then you could change the brand of food or give her food supplements.
There are illnesses that cause aggression. Most widely known and most dangerous is rabies, but there are many more infections, parasites and illnesses that can influence the behavior of an animal.
If there is rabies where you live and she attacks all other dogs and even you, you must be especially cautious. There is no cure for rabies. Every dog and human that gets infected dies. The only protection is vaccination.
A vet should analyze the blood for signs of such illnesses. If that's the case, you must separate her from everyone else in a way that the other dogs cannot come into contact with her saliva. They must not be able to eat or drink from the same dish and they must not be able to lick any item she was in contact with. This is not prison, but quarantine. It's not to punish a dog, but to protect all the others.
Stress / Burnout
Living with so many dogs and having puppies regularly sounds like a lot of stress for a dog. Dogs can have Burnout and PTSD like humans. Maybe she is so stressed that she kills the puppies to reduce the level of stress in her environment.
Life is never straight-forward and simple. A combination of different factors could have caused her to kill the puppies.
She might have had a mental disorder from birth (due to inbreeding), but only recently started to kill puppies due to stress or her age (many mental illnesses manifest or get stronger at a certain age).
Or she could have been in constant pain for a while now, which caused her to eat less, which caused a malnourishment, which made her kill the puppies.
Any combination is possible.
What should you do?
If you let your dogs breed like that, you risk that this dog is not the only one who suffers. I suggest you find a way to control which of your dogs breed. You could desex all of them or just a few and let them live separate from the others. Make a family tree of your dogs and make sure that no siblings or parents and children breed with each other.