Honestly, I wouldn't put down the dog either.
If no one else would take care of it, at best i would make sure the Dog and child had no further contact. None of it was actually the problem of the dogs... mostly just the parenting.
It's not the dog that needs to change, but the owners.
If it was for example a 10 year old doing the same thing, I wouldn't put down the dog either, it was 10 year olds fault. If you provoke an animal you general get what's coming to you... just because your niece is young it doesn't shift blame to the dog, just the parents. Punishing the dog for the parents mistake would be wrong and generaly immoral.
As for the droopy eyelid. Hopefully it won't be that bad. I had a similar condition due to being born premature, hardly ever got noticed unless i pointed it out.
