Wow. Lots of posts.
No to cognification. The concept of a cyborg child is almost too ridiculous to be considered. Unless we wanted like a jester or something.
Mutation, yes. It's consistent with our mind set so far. We could let her choose or let Gamington and Cerulean choose. Doesn't really matter.
Let Gamington and Cerulean have free reign in choosing exactly what to do with her? No. What would they do? Let her hang around our base as a human? That's hypocritical and unless we change our no human rule it's not an option. Let her leave? With knowledge of our operations and us that could be divulged to our enemies? Absolutely no. They can choose what she mutates to though.
By all means go up to the two conspirators and have a talk. Explain our reasoning so everything is nice and clear.
These children NEED to be mutated. They are living at our base and thus must adhere to our rules. One of those rules is monsters only. If it means a lot to them, in the future we won't pick up any more kids but unfortunately the fate of these kids was decided the moment they walked into our base of operations. Remind them of the alternative. Where could the kids still be. Not any better than where they are now. Sure they went through pain but now they will get all the proper love and respect that comes as being a part of the InCognito family. Sure they might die on combat but that's a risk we all take. Even InCognito himself has been in the front of the action putting his life at risk. At least here they get treated well after the painful mutations. No so much where they were before.
Don't discipline them. Warn them. Next time come to us with their problems, don't work behind our back. We might be able to come to a compromise solution that makes everyone happy but even if we can't, we'll at least explain why we are doing what we're doing. They can be our moral compass. We might even listen to them a lot. The END DECISION THOUGH LIES WITH US. Caps for forcefulness. It's the truth.
Also we no longer need that school teacher and she's a pain anyway. Go tie her up and bring her to Chemistra. Say,
"Kill her now. I want you to do it personally. To prove a point. So you know. That'll be all."
Walk away.