Hello! Thank you for posting a plea, I can explain the bans to you.
The name "Killconey12" was banned because it is unfortunately pretty similar to a fairly serious "meme" from a few years back, and having players join servers with "shock-factor" names is more common than it should be. I have done some research into it and I do see that the name comes from that book series you mentioned.
Your account was banned immediately just because we don't allow alternate accounts, and seeing that an alternate account of someone who we previously banned for being a probable "troll", we strive to get them off the server as soon as possible. We work quite hard to ensure that we're as safe as can be for our players, and that's one of the ways we look out for them.
I will unban you and your daughter, but multiple staff questioned if her name was okay, as even ignoring any similarity to the "meme" mentioned above, it could be interpreted as a violent statement instead of the innocent name it actually is. It would be ideal if she could use a different name instead, as I'm sure players and parents of younger players could also assume the name meant something else.