amen to that....that "friendly" neighbor's advice to you sounded more like a warning....I'd launch one back at her letting her know her dogs' presence on your grounds will NOT be tolerated since she's already told you they kill chickens and cats. Buy a rifle and practice with it. Let your neighbor know SHE is the one responsible for confining her dogs to her property and if she fails to you will address it as you see fit on YOUR property.The first thing I'd be doing is looking up the local laws on letting dogs run loose. I'd print off the pages pertaining to that and politely deliver them to said neighbor. Then I'd politely tell him/her that if the dogs were on my property they just might not show up at home again. If you're Against shooting them then the first time they're on your property coax them into a garage/shed & call Animal Control to pick them up. If there's no AC in your county take them to the nearest shelter or Humane Society.
I know NO WHERE in the entire USA where it is permissible to let KNOWN stock-killing dogs run free & kill whatever they like.