Manage Phone Audio Player through Car Stereo over Bluetooth
Highly depends on the bluetooth profile and capabilities of your stereo. Some only implement call button profiles, some implement audio only and some support audio and buttons. Some have advance support for Playlist and file system. A FM Bluetooth adapter I had could play and stop my music but couldn't see play lists or anything.

If you press the play button twice does it work? Or long press? If you play your music, do the buttons play at that point? But in any case, there is no way to really change it, without replacing the stereo.