CarPlay not playing nice with iTunes

I have a new 2017 Volt and a large amount of music on my iPhone 6 that I listen to mostly on the cloud through iTune match. I'd like to have full access to my music through CarPlay. The problem is, when plugged into the USB port, I can only see my entire music library (in CarPlay) if the car is in Park, though it is all visible through the car's Audio mode. When the car is out of Park, CarPlay will only show Recently Played music. In any case, even using the car's Audio mode, only some of the songs will play. Many songs won't play at all or will stop in the middle. It will then usually revert to playing music in shuffle mode. Any idea what's going on here?