X2Sorry about your lost chickens. I do understand your frustration. I also get that accidents happen. Other than keeping the dogs and chickens separated as you are doing now, and attempting to work with them, I don't know what else you can do other than take them to the pound since you haven't found anyone to take them.
Nobody is meaning to berate you. And yes, I understand your frustration also.
Sounds as though, however that the problem isn't with the dogs or the chickens but lies with your son letting the dogs loose and leaving them unattended.
I understand also that you are needing to vent and trust me we have all been there and done that. Still you need solutions. Secure the chickens and leave them secured as long as the dogs are on the property. Hot wire your coop and run, Stress to your son that he cannot let the dogs out and the next time he does, the animals will be taken to the shelter and or, put a lock on their gate so they cannot be let out.
I seriously do feel sorriest for the dogs. Unwanted and unloved is a terrible fate for any dog. They can share the same space with chickens without bloodshed. It won't be easy tho and everyone has to be willing to make it happen.
I seriously wish you good luck with your problem.