1) the Apple Remote uses IR - light outside the visible spectrum - whereas Wi-Fi uses radio technology, so the two can't possibly physically interfere.

2) on the driver level, there is no connection between the driver for the Apple IR Receiver and the Wi-Fi driver, so I can't see how they'd possibly interfere with each other

3) I'd usually suggest to exchange the Apple Remote battery - and you might still give this a try just to rule this out as a possibly factor - but IF the Apple Remote works consistently (!) reliable (!) otherwise, this may not be necessary

4) looking at the big picture, the only difference between working and non-working scenarios is that the non-working scenario involves a mechanical device - which could possibly have physical effects that might interfere the IR spectrum used by the Apple Remote to transmit commands to the Mac's IR Receiver. This is what the Apple Remote sends for a single button press:

[IR command: button X pressed] 
[IR command: repeat] 
[IR command: repeat] 
... 
[IR command: repeat] 
[IR command: repeat] 
[IR command: button released]

After receiving a [button press] command, Remote Buddy expects the [repeat] commands to arrive within a certain time frame. If it does not arrive, it treats the button press as if it had ended. So if even a single one of the repeat signals gets corrupted due to IR interference - and can no longer be decoded by the Apple IR Receiver due to that - the button press will end at the end of said time frame.

Chances are the mechanical device you're using is emitting infrared radiation, thereby interferes with the Apple Remote's IR signals and leads to the premature end of the button press.

When looking for possible IR sources that might interfere, keep in mind that heat can also be a source. More here: https://en.wikipedia.org/wiki/Infrared

5) Another possibility would be that you're trying to use the Apple Remote from too far a distance or that there's not a direct line of sight when you try to control the mechanical device.

6) Other options that aren't vulnerable to IR interference would be Remote Buddy Mobile (Wi-Fi, free on the App Store) or a Sony PS3 BD Remote (Bluetooth, sells for around 20€).

Hope that helps.