Hi,
I've done almost exactly what you are talking about, and it doesn't need relays or optocouplers. It's just a matter of finding the right place to intercept the signals. There should be a chip that takes in the RC signal and puts out signals for the motor control circuit. You seem to have identified those. So all you have to do is intercept the signals between the chip and the motor driver circuit. Put the chip outputs on arduino pins set for input, and then use some arduino pins in output mode to control the motors. Your sketch would periodically check to see if there is any input, and if so, switch to "remote" mode. In remote mode, program the arduino to just pass on the signals.
The power issue isn't that big a deal, really. Run your arduino from one battery, and leave the RC car power system as is. Just be sure that the GROUNDs are tied together, or it won't work. If the chip is really 3v, then you might need a resistor on the output pins to drop the voltage down.
HTH,