Thank you all so much for your concern. I don't know yet what today's outcome has been. The duck belongs to my friends, and they are making the difficult decisions--they and I have been busy today and I haven't heard yet what they are doing. I will update as I'm able.
In the mean time, I totally get what everyone is saying. I have euthanized an animal on occasion when I believed its quality of life would not be worth the pain and suffering of recovery. I believe my friends are more concerned for the animal than for themselves--they want to do what she would want, not what they want.
The lady at the waterfowl rescue listened to my description of the injury, which I gave in gruesome detail, and she said that they've seen birds with similar injuries and worse that went on to live happy and basically normal lives after recovery. She recommended that my friends bring the bird in immediately and surrender her to their care (which means that my friends will have to give up their pet, but like I said, I believe they are more invested in her welfare than in their attachment to her), and that they would do what they could. They have an amazing program down there with outstanding experience, expertise, and veterinary access. Like I said, I don't know why I didn't think of it earlier.
And if they're not able to save her or if her quality of life is likely to be low, they will be able to let her go in a quiet, peaceful way using the best techniques for euthanization.
Like I said, when I talked to my friends last, this seemed like the best course of action but I haven't heard the outcome yet.
Also, thank you for those who are concerned for the son. I feel awful for him. He is a sweet, sensitive boy who loves and cares for those ducks better than most kids are capable of caring for a dog. He knows everything about each and every one of them, including what shape each one's eggs are and every little quirk. Add to that, he feels emotions very strongly and also feels his own responsibility for things very heavily. So I know he is heartbroken and feeling just terrible about the incident. That was actually my first worry when I heard what had happened. But he will be okay in the long run. He is lucky to have the wonderful family he belongs to--they will help him deal with his emotions, and he'll be fine. It's just hard right now. So, anyway, thank you for thinking of him too.