Gosh, what a terrible tragedy for both families.
Your daugher and the rest of your family must be devestated. I am horrified to think that your brave little girl could have been mauled. You should not have to worry about *how* you keep your own animals on your own property. Dog owners do not have the right to rely on *you* to lock up your animals to protect them against *their* traspassing animals. You should be able to free range your chickens (or any other animal) on your own property. They have no defense whatsoever and no judge would side with them if you asked for compensation.
But I think that other family is probably devestated by the loss of their pet too, and were probably reacting in their horror of losing their beloved. I wonder if that was the first time he got out since you didn't mention he was a chronic problem. Maybe they'll apologize...ok, maybe I live in La-La-Land, but one can hope that after they calm down they will see how unfortunate this whole situation was and how terribly wrong they are to blame you. It's so painful losing a pet (for everyone), as you well know. But unfortunately, they need to own this.
I'm a dog lover too. I have six huge dogs. I would be unconsolable to learn that my dog got out and mauraded over at a neighbor's place. But it's my responsiblity to keep them in. If my dog was shot on another person's property, I would be terribly grieved. I would be angry if they shot any of them out of pure spite (because my dogs are all out with my livestock and are accostomed to them) but there would be nothing I could do about it. Tresspassing dogs often get shot. I've had to keep a loaded gun out for a neighbor's dogs who daily come to pick off my chickens one by one myself. We all do what we have to do.
As to their comment about chickens being replaceable: unfortunately, a lot of people think like that. But the *value* of one animal over another animal is not what this is about. It's about one's rights over another's. Their rights end where yours begin, and you have the right to protect yourself, your family and your property. They need to keep their dogs within the confines of their own property and stop causing havoc on yours.
About asking for compensation, that's up to you. I haven't asked for compensation when I've lost chickens even if offered, because in these people's minds, if they compensate you for the loss, then they're excused from the event and it'll happen again. At least with my neighbors. But you're well in your right to ask, and if it goes to court, you will get it.
Good luck and I hope everyone starts healing and finding their common sense (in the case of your neighbors). My prayers are with both families.