It's not good practice to use a webpart within another webpart. You use the controls because you don't need the additional overhead of another webparts code not to mention your page type or any other code you've written is dependent on that webpart being installed. This is why I suggested looking into the inner-workings of the original webpart.
A good example of this is you install a third party webpart and make a reference to it in another webpart. Now when you need to export your custom webpart you won't have your other 3rd party webpart because of this. So you have to remember to export that as well. Or a better solution would be to use the built-in controls that are already there and you know won't be modified. I'm not saying this is how it has to be, I'm saying it's best practice.