At WINE HQ, there's a list of supported applications. It is not obvious what will work in WINE without trouble and what won't.
For instance, I've recently discovered Internet Explorer is WINE-able (useful for Web Developers mostly, perhaps Users if they have to use non-FF site). An expensive Chess program I have, which was a Win95 one and should be simple, doesn't.
So check that, but don't let your Dad see that this is pointless as you can circumvent the controls very simply...
On the original issue, as noone had any "real" suggestions, I think you ought to ask your question on the TV time mailing list or forum. Perhaps if your "Parental Control" scheme is simple enough, some developer will pop up and say "Easy..." and you will get a patch to add the requriment; though expecting it to be GUI controllable is unrealistic.
What I mean is , if certain channels are barred after 9pm or all day, or all channels... It'd likely be simple to use a script to check an access control, called from the application, that used some simple text file format (prefarably XML with view to later GUI support). But what you have to understand is that this stuff is really rather broken, in the context of a Free OS, so may not interest "real" developers.
PS. I wonder what your Dad watches that he don't want you to see? :lol: