You have already tried talking sensibly to her, and she still refuses to take appropriate action.
Start a file. In it record the dates and times of the attacks, what type of dogs were observed and what livestock they were harrassing and what livestock was maimed or killed.
List in there the dates and times of the conversations with the supposed owner of the dogs.
List the dates and times that you have notified the authorities of the incidents and what, if any, action was taken by them to resolve the issue.
Any livestock that was killed by these dogs need to be listed. You will need to include the original purchase price, the cost of raising them up to production levels, the cost of replacements.
You will also need to project the loss of income from the deceased animals. That includes the eggs and chicks from the birds, and the kits, fur and meat from the rabbits. Also include any Vet bills that you have incurred as a result of the attacks.
Get a copy of the local ordinances and familiarize yourself with them, make a copy for your neighbor and highlight the parts that pertain to what your rights are as a livestock owner.
Write her a letter that explains you position calmly and rationally, and that if she doesn't control her animals, that you will take what steps you are allowed to under the law to protect your livestock from future harm. That includes shooting the attacking animals if allowed by law. Put the highlighted copy in with the letter and send it certified mail, return receipt requested. Put the signed receipt in the file with your copy of the letter.
Some states allow up to triple damages for livestock that are destroyed by someone's dogs. Alot of communities now have dangerous dog ordinances as well.
The purpose of the file is so that if you have to go to court over this issue you will have proof that you have done your part to make sure that your animals were contained properly and that these dogs invaded your property and willfully attacked your animals. Include any photos that you have taken either of the dead animals and the destruction they caused or of the actual animals themselves while they are attacking your animals.
Make copies of everything in the file, keep the originals for yourself and have copies ready for the attorneys and the judge.