I've been working w/ the PS2 remote and the RS 15-2116 because it was behaving strangely for me too. It looks like the it actually uses two differents subdevice codes, one for the DVD buttons and another one for the gamepad buttons. Chances are you have the DVD buttons but not the gamepad buttons.

Try learning the gamepad buttons, see how they behave in the situations that are causing problems, and then put them on keys where they make sense.

I had problems learning the arrow keys because they actually send out a two signals, one for the DVD and one for the gamepad buttons.

If you have a JP1 interface, I posted a device upgrade that you might want to take a look at.