You're on the right track. You could use a switching regulator for better efficiency and less heat. Adafruit has the official recharging resistor values in their FAQ.
Your schematic is drawn pretty confusingly, though, so I'm not sure if it's right. Can you label the pin numbers of the dock connector? Generally a linear regulator is drawn like this:
Of course the function is the same no matter how you draw it, but readability counts. :) (Also, in a real AC-to-DC power supply, you need to lay out the PCB in this specific way, or you can have issues with ground current noise getting through to the output.)
Your car voltage will be varying due to different things using the battery at different times, possibly with a fast enough variation to be in the audible frequencies. Your regulator will be dumping current to ground in order to keep the output at a stable voltage. Since the difference between the stable output voltage and the fluctuating input voltage is not constant, the current it shunts to ground will also be fluctuating. Since copper is not a perfect conductor, this ground current flowing through ground traces back into the battery causes the different points along that trace to be at slightly different voltages, varying at audible frequencies. If another part of the circuit uses a point along that trace as its ground reference, it will see that slight voltage variance as a signal, and the noise will get into the audio (small buzzes or whines or clicks at low volume). This is why the layout of PCB traces matters. The ground traces should be laid out in the same shape as the schematic, and your other circuitry should only be connected "after" the output filter capacitor C2:
There's also noise from the iPod. It draws a lot of current while charging, up to 1 A peak, but like any digital/computer device, the current is intermittent (repetitive spikes from refreshing the screen, moving the hard drive head, etc.) In your schematic, this isn't a problem, since the audio ground is separate and not touching the charging ground.
I would say it is very very dangerous for iPod. Eventually it might die instead of reset.
This must be the transient spike going through USB.
So, I would take a look at it at oscilloscope.
And before that I would switch to separate 12v->USB adaptor, not the bundled one.
Best Answer
The iPod normally uses USB, Firewire, or serial when talking to other devices, like your car. Pin 21 is used by the iPod to detect what it's plugged into, not by the car to detect when the iPod is connected. We simply don't know what will happen when Pin 21 is disconnected, but I'll make an educated guess and say that it won't make a bit of difference.
Odds are that your car uses the USB port to talk with your iPod, and detect that the iPod is present. If you disable the USB port (by clipping the wires, for example) the car won't detect that the iPod is present, and thus not enable the iPod as a valid audio input. In short, it probably won't work.
I used to have a car with an iPod dock. When connected, the iPod controls were disabled, like yours, and the car's controls were absolutely terrible to the point of being unusable. So I feel your pain. Now, I won't ever buy a car or car stereo with a device specific MP3 player connection-- just a standard "AUX In" for me.