Good fences make good neighbours. My dog shouldn't be able to get out, so my neighbours dogs shouldn't be able to get in. But stuff happens. My chickens free range within a large electric net area. A couple of neighbourhood doga are jumpers. If a dog comes over my boundary fence, my dog intercepts it. I've caught neighbourhood dogs in my property playing with my dog. I've also seen her sending them packing in fear of their life. She seems to have good judgement on who is who and she loves us, the chickens and our cat and protects them above her desire to play. If a chicken gets out of the netting, she will come let us know. Unless the chicken makes it to the door first.
Shooting dogs harassing livestock or worse is completely reasonable. Especially on a second offence. It's understood and accepted where I live, also legal to do. But it's also local courtesy to give one chance unless the livestock is particularly valuable, or the dog looks like it might be a wild dog. Financial compensation for the loss isn't asked for. It is offered generously as a matter of courtesy.
An example of where a dog would be shot on sight is if it is harassing an expensive horse in a way that it could injure or cause the horse to injure itself. No second chances. But poultry isn't in the same category. Emotional attachment has no weight in livestock terms. So a second chance is considered courtesy.
The laws where i am:
You have the necessary firearms licence and use the firearm according to state firearms laws.
You reasonably believe the dog is attacking, or is likely to attack, your livestock and is not under someone's control.
You live on land that is subject to a rural fire levy.
You comply with other laws
The key word in this is livestock. If they aren't used for commercial purposes, they probably won't be considered livestock. But commercial purposes is an easy bar to cross when it comes to poultry.
Unfortunately you've now announced that's what you will do. Imo cool heads always prevail. Inform them of what has happened. If its enough money you wont let it go, Give them an invoice for the damage if they dont offer. All very business like. If they dont pay promptly, dont pursue it unless its quite a lot. So when it happens a second time those dogs just don't come home that day. Which is the same courtesy, or lack thereof, they provided you.
Now if they go missing and they are her babies, you are going to be the first place they visit.