OK ~
We have a daughter who put herself in harms way to save her pets. I would have done the same thing. Thinking of my pets and not myself. Thankfully she was not harmed.
Had the dog bitten her ~ I don't believe for one millisecond that the dog would have bitten her because it is a GS or because it was a vicious dog. The dog was after anything that was moving and could have (and thankfully it didn't) gone for her arms, legs, face, etc. At that moment I don't think the dog would have been able to rationalize the difference between a moving arm or a moving chicken. It's the nature of a dog. It had nothing to do with the breed of the dog but the size of the dog. Had it been a smaller breed dog...it might would have had a different outcome.
The owners of the dog ... I feel, had a normal reaction to the loss of their pet ~ who probably have never seen it act that way and can only remember their family member who wagged his tail, chased a ball, and slept with the kids at night. Had they been there in person to see what was happening at the time, they would probably have a better understanding of why the dog was shot.
We've seen everything from you killed my dog for no reason ~ it was just a chicken to these chickens were loved and named by a daughter to an irresponsible dog owner because the dog was loose and attacked the birds. (Which the OP has indicated that this dog did not appear to be a dog who was allowed to roam all the time stirring trouble).
The OP feels quilty because she let the chickens out for some fresh air from the rain and mud and are dead. That's normal. The dog owner probably feels guilty because their dog left their property and is dead. That's normal. Both side are feeling anger and hurt against themselves and against each other. That's normal.
Who knows what the outcome will be. Hopefully it will be handled in a civil manner. Right now, the important thing is to help the daughter get over this ~ maybe get her some new chicks. And most of all, to eliminate all this blame when we really don't know anything about the other family and their dog. Offer support to the OP and drop the labeling of dog owners and the breeds of dogs in every case of dog vs chicken.