I'm not clear on what you mean by "a small speaker that acts as the reciever."?
It is possible that the car computer uses a "bridged" audio output, where both ends of the speaker are driven out of phase by two audio amps (to get more audio at a low supply voltage). If you just connected to the two wires that formerly went to the internal speaker, you would have two problems:
1. The input to your main stereo is ground referenced, so connecting one of the wires to the RCA jack AUX input would short to ground the audio amp inside the computer.
2. The other audio amp with got connected to the aux input has a huge DC offset in it. If the aux line input doesn't have a DC blocking capacitor in it (inside your stereo), then you need to put one outside...
I dealt with these exact same issues in extracting the "*****-in-the-box" out of a Garmin 496 GPS. I ended up using an audio coupling transformer to convert the floating, bridged, balanced GPS audio output to the ground-referenced, unbalanced, audio input to an audio system...
I needed to do this to break up a ground-loop to get the alternator whine out the audio, but that is a separate story