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.
Best Answer
"Lightning" is Apple's proprietary connector. There is a cryptographic transaction between the dock and the device, so you need to sign up to Apple's licensing programme to build devices that interoperate with Apple devices.
References: