GNU License, Again

[mike3]

Hi.

I just noticed someone with concerns a bit similar to mine, and
although I posted a message there I'd like to post another here to see
if I can be more clear and/or make it more visible.

Here's the scenario:

I have two programs, a GPL program and my own program, to which I
myself own the copyrights. Now, I take a couple of pieces of the GPL
program and install them in my own program, and then release the
resulting package under a proprietary or other non-GPL license, BUT I
go and also include in that package AND in another source like a
website whose access does not require buying or otherwise obtaining
said package, ALL of the GPL code that was used, licensed _under GPL_.
Even better, I put that code in a form (like a DLL) that is _separate_
from the non-GPL part(s) of the program and hence, could be easily
separated from the non-free program and the non-free program
distributed in a non-free way while the free code is distributed in a
free way compatible with GPL.

So, would this be permissible?