Lots of negatives above, so here's someone who has had several cats de-clawed over the years and we're happy about that. I'll give a few pointers.
1. Yes, de-clawing is surgery that leaves the cat with sore toes for a short time (1-2 weeks??). They did not show obvious signs of pain for more than a couple of days. After that our cats have never shown any discomfort or concern about their feet.
2.When it is done, you need to pay close attention to their littler box for at least a week. We replaced the common clay-based litter with the stuff made from recyceld old paper and changed it completely - every day or two at first - to reduce the chance of infection.
3. The last couple of times it was a situation of 2 or 3 new kittens at once. We waited until they were the right age / maturity for neutering / spaying, then had both that surgery and the FRONT-only de-clawing surgery performed at the same time on all of the group. So they recovered together. Slight price reduction on dual surgery for three kittens at once. Oh, and here the vets also will install an ID chip (under the skin on back beytween front shoulders) at the same time and provide a certificate of this. The city here will waive yearly cat permit fees for chipped and neutered cats, and issue a good-for-life free pet permit. We have NOT had it done on a fully-grown cat, so no experience there.
4. Our plan for these cats always was, from the start, that they are indoor-only cats. They never go outside. So we don't worry about their ability to defend themselves against others or predators.
5. Our daughter had one bad experience with this on one cat. Apparently the vet made a small error in the work and left a small bone chip in place which did cause the cat significant discomfort and possibly infection. Took a little while to understand the problem, and a second small surgery for no charge to fix it. No extra cost, but a bad experience for the cat (and owners).
6. There are two common forms of such surgery. One is to remove from the tiny end bone of each toe the claw and nail bed from which it grows. This CAN fail sometimes of not all of the nail bed is removed. The other is to remove the entire tiny last bone in each toe. We are told the cat really does not use that bone for normal walking, etc, and this type of surgery does no harm and is more reliable than the other. We chose the latter.
7. As far cat behaviour, they really don't know about all this, of course. Their natural instincts are to scratch stuff, and to use the calws for gaining a solid grasp of things as the move, jump, land, and grab things. They learn very qickly that their ability to grab a solid hold on things with the front paws does not work as well as they might hope, so they adjust their actions in a short time and never know the difference after.
8. After this removal, the BACK FEET are still dangerous! So don't ignore that possibility when handling them or having them leap from your lap.
Our cats are happy and spoiled kitties. We are very pleased that the furniture is not being damaged, and neither are we (by accident) being scratched very often. By the way, I think your fear of damnage to your child's eyes is exaggerated, although anything is possible. It is more likely that injury will be to other body parts less disastrous, but still painful. That is part of teaching your child how to handle a pet gently and responsibly. Such habits also can train the cat that people (even small children) can be trusted to be kind and gentle.