What you are seeing is how iTunes stores song files on the iPod to optimize how the iPod operates as an iPod (not as a song storage device for your car audio system). You cannot change how iTunes syncs songs or how the iPod accesses them. Some car audio systems are designed to understand how songs are stored on the iPod; you should consult the user manual for the car audio system.
If you manually change how the songs are stored on the iPod, it will no longer operate properly as an iPod. Instead, I suggest you buy an inexpensive USB flash drive, with many times the storage capacity of a 2GB iPod shuffle. On the USB flash drive, you can create folders and manually store your favorite songs as desired. Then, leave that USB flash drive connected to your car audio system (instead of constantly connecting and disconnecting your iPod), except when you want to add or change songs. Here's one that barely sticks out of the USB port
http://www.amazon.com/SanDisk-Cruzer-Low-Profile-Drive-SDCZ33-032G-B35/dp/B00812 F7O8
Consult the user manual for the car audio system for things like supported disk format (of the USB flash drive) and audio formats (of stored songs).