Let's see
1) Viscious dogs at large
2) Unable to contain said dogs on their property
3) Injury to you "docile" pets
4) Potential for neighbors dogs to attack you or family members

5) Solution- Shoot them. Numerous warning have been given both by you & Law Enforcement. As long as you have not said to LE or Neighbor, you would shoot the animals follow deadly force guidelines
Threat, or what you perceived to be a threat constitutes use of deadly force, AS NECESSARY!

You do what you think is right. HOWEVER after more than one Viscous attack on your "Family pets" I'd say you have more then good grounds to do what is necessary.