So after experimenting a bit, I came to the conclusion that the best way to do this, was to create a skin which loads different .inc files, depending on which 'page' the config skin is on. This seems to be the same way that Kaelri has done it in his package.
My problem is this: the InputText plugin doesn't seem to work when used in a .inc file (Appearance.inc in this case). It just won't do anything when clicking on it on the skin. The weird thing is, I'm sure it worked a couple of days ago when I started working on it.
Removing @Include3=.... from Config.ini and copying the contents of Appearance.inc into Config.ini, will make everything work.
Anything below this line is only to clarify my problem and if you've already understood it, there's no need to continue reading.
In case I haven't made myself clear, you're welcome to take a look at my code and hopefully you'll understand what I'm trying to do and what my problem is.
Here's my code: (I've left out some of the unrelated code..)
Config.ini (Displays background and will have buttons to change the #CurrentTab# variable in ConfigVariables.inc.. CurrentTab in this case is Appearance.inc)