I would not punish the dog. Sounds to me like the old dog just lashed out, not intending to kill the kitten. I would chalk it up to old age and bad timing. I would keep the kitten far away from the dog, even if you are near. It would take only one second for that to happen again.

I have a dog and three cats. They mix it up sometimes, but my dog is AFRAID of the cats. Prue, the dog, still goes after them if they are in the kitchen while food is being prepared. She herds them out of the kitchen by barking and going after them. It is her way of protecting her chance of getting food and not wanting the cats to have any part of it. I allow it. I don't reward her for it, I just don't mind her getting the cats out of the kitchen. They can be a pain in the butt when preparing dinner etc.

My heart goes out to you and your family. I imagine it will take years for you all to get that moment behind you. Forgive your dog, get a new home for the kitten, fast and let the 12 year old live out its life as it was before the kittens arrived.

Lesson learned.