I'm very sorry that this happened. I am more sorry that the dogs have been at your property twice in 3 weeks. I understand wanting to be good neighbors but I don't think that I would be accepting of an apology no matter how heartfelt it was. We recently found 2 of our neighbor's dogs in our pasture after they killed several of our chickens. The neighbor was talked to and said that he will keep them chained.
I think that killing chickens is one thing. I do understand that dogs will be dogs at times (I do NOT think that a dog that kills anything should be able to get loose). But these dogs came and attacked your dogs. That makes them "dangerous dogs". I worked in animal shelters and vet offices for a number of years and this behavior is unacceptable. A dog that is going to roam and attack other animals outside of it's home/land may well expand it's "prey". You say that you have kids, I would be concerned that if these dogs get loose again and your kids happen to be outside or go outside if they hear fighting that they could get bit. Even the most friendly to people dogs can bite when hurt or caught up in the moment of fighting/chasing/killing etc.
If you have not, this should be reported to the local authorities. Most likely nothing will happen but at least it has been reported. I would be very worried that they will be loose again. What happens the next time they are out and won't come in and whoever is home has to be somewhere? I am not trying to make you feel worse or saying that you shouldn't try to work with neighbors but our neighbor now knows that if his dogs are here again, they will most likely not make it home. After talking with other neighbors, we found out that this same family has had several dogs that were shot by neighbors after killing/harrassing their livestock. And these dogs in particular killed some sheep in a pasture. (They are Great Pyrenees too so just because it's suppossed to protect livestock doesn't mean its safe) Some people should not own animals as they have no sense of responsibility.
I know that money will not replace your birds but sometimes that is the thing that will make people realize they need to change. Hit them in the pocket and not just replacement value. Replacement, feed costs etc.
On a side note, we did not call the sheriff when the dogs came but we did talk to a deputy when we were out the next day. Here, if we had reported it and the dogs were out again, it would be a felony. We were also told that we were within our rights to kill the dogs and our neighbor understands this.
Again, I'm sorry for your loss and I know that I have a different opinion than many you received but I would hate to see that it happened agai