Instead of euthanizing a dog that bites, why not have the dog's teeth extracted?
Many years ago my little dog, Wee Hans of Cybalo, died of old age, though he had lost his teeth before and was OK the few years he was toothless. He had to have a soft diet, but he didn't seem to mind.
If the dog that bit the two women goes to its final resting place, there will be other persons affected by its plight: the reason being that there should be a humane solution to this animal's fate and justice should be done so that the injured parties are satisfied and the owner is not deeply hurt by the loss of his pet.
I hope that someone has a better idea.