To control the wifi-less TV, you need infrared signals such as those shot out of classic remotes. There is add-on equipment for iDevices to provide that capability.
However, keep in mind that iDevices are often mobile devices . People tend to want to take their iDevice with them when they leave the house. You posted the warning word of "We" in your last post. I read that to mean that more than one person lives at your house. Are you going to leave that iDevice behind when you leave so that the other person(s) in "We" are going to be able to control the TV with the "good remote"? If not, you probably should be thinking about a good learning remote such as those from Universal Remote Control or similar. I have their MX-850 learning remote and I think it is excellent for the "one remote to rule them all" purpose. If you really want a touch screen remote control, those are available too (but I know many home theater people who prefer physical buttons they can feel in the dark rather than leaning on a flat screen remote).
A dedicated remote makes sense to leave behind in "We" households... much more so than leaving an iDevice behind for the rest of the "We". Then, consider making your iDevice capable of being an additional remote if you really want that benefit. By not getting the rest of "We" dependent on your iDevice, you won't get the grumbles/gripes when you take the "good remote" out of the house.
I know there's the whole "cool" concept underpinning using an iDevice as a remote control but it really becomes an issue unless the person doing it is single, living alone. Remotes also tend to get sat on, dropped on the floor, etc- none of which tends to yield a positive outcome when it's an iDevice.
Lastly, some set-top boxes have an app companion for controlling them. For example, DirecTV whole home DVR has an app that replicates the remote functionality for controlling the DirecTV Genie box. It works over wifi so you wouldn't need the infrared add-on device. See if your set-top box (cable? Satt? etc) has such functionality and that might be another way to go.