When you connect ANY iPod to a car audio system using a USB connection, the iPod is acting as a storage device. The iPod is not doing anything else. It is not being controlled to play music. The car audio system is only accessing the iPod's "disk," like it would access a USB flash drive that has song files on it, and the car audio system is then playing the music.
The most likely reason it does not work with the shuffle is because the shuffle does not have a dock connector (or Lightning connector) like other iPods. It uses the headphones jack, so there may be some missing functionality or connection points. You should check the documentation for the car audio system to see what devices are supported.
If you connect the shuffle with the appropriate cable to an auxiliary audio input on the car stereo, you are using the shuffle to play through the car speakers, like with any device you connect that way.
As an alternative, you should consider getting a cheap USB flash drive, like this one that is so small that it barely sticks out of the USB port
http://eshop.macsales.com/item/SanDisk/SDCZ33008G/
Put your favorite songs on it, and leave it connected in the car (except when you want to change songs). It has 4x the storage capacity of a shuffle for about $10, and there's no dangling cable. You'll save your iPod from the wear and tear of constantly connecting and disconnecting it, plus a USB flash drive is much less susceptible to damage from extreme hot and cold compared to an iPod (especially one that has an LCD screen).
