
I know some people treat their chickens as pets, and a vet visit might be something to consider. Where I live, the vets don't know much about chickens, and it would cost you $$$ for nothing. I would never consider taking any of my chickens to a vet. For the price of one vet visit, I could replace my entire backyard flock 3X over! Not kidding.
I would much rather harvest an injured chicken myself. If a bird is sick, however, I will not butcher and eat it.
Having the ability and skill to process your own chickens is a great advantage. Many people have the opposite problem of yours and they cannot get themselves to butcher their chickens.

Obviously, I don't know all the small details between you and your mother, but it sounds like you did the right thing to me. Assuming, of course, that the rooster was yours and not your mothers....