The device you are describing doesn't sound like what you want. The number of functions mapped to buttons on your remote is limited by the number of channels your alarm system is capable of controlling. Most two button remotes are capable of sending three different signals (A, B, A+B), so if your alarm can operate on three individual channels, you can program each of three buttons to a unique function. Some remotes can have additional channels using two buttons (i.e. pressing the A button momentarily is mapped to a different function than pressing the A button for 3 seconds).
So to make a long story short, i don't know how many channels the factory alarm unit has, but if you have an unused channel, you should be able to program it to activate your door popper. If you don't have an unused channel, or don't want to give up an existing function, you can buy aftermarket alarms with additional channels.
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