From your perspective, your points are solid, and I do appreciate you actually taking the time to look into it. With that said, I have a few things to note.
Your concerns are valid and thorough, but server logs don't give the full context of events. I'm unfamiliar with the software/logging system you use to identify who built what (eg, if usernames are shown for each block edit, or if you have to look up a given user's block edits to see exactly who made what changes), so I'm compelled to point out that "alainjvd" was not the only contributor to the house. It was a short while ago now, but I believe we had three or four contributors. "alainjvd", of course, "rayneawesomegirl", "spooker6" and MAYBE "Kirstae" Your second point can be explained by a dynamic IP address. Without knowing exactly when your logs indicate the IP address change, I can only speculate that it was due to the recent squirrel incident. Any loss in power to the modem causes a change in IP address.
Conceivably that could be the reason, absolutely. In reality, I don't see the point in wasting your time, or mine, with a futile appeal that, at best, will have to be re-appealed in a month's time. In all honesty, I may never appeal it, since I felt I was spending far too much time playing Minecraft and the ban will likely be good for me.
Ehhh... I guess reaching over her shoulder to type nonsense can be constituted as using it, in the strictest sense. I believe this excerpt, being posted without context, gives the impression that the entire account history is like that. As you'll note, there's a quick transition between writing styles, vocabulary, response time, and coherence before and after the excerpt. I sure haven't ever sat down and played on her account as I would my own. She saved up her allowance for a couple of months to buy herself an account, so, no, I'd never knowingly do anything to compromise her ability to play wherever she wants.
With that said, if you still feel that I am likely to abuse her account to bypass a ban instead of just buying a new account and playing through a tunnel, then I do completely understand. As I said, I can certainly understand your concerns from your perspective - they're thorough and solid - and all you have to go on is your perspective and my word. Either way, thanks for taking the time to look into it. It's a lot more than most server admins would do.