I'm not sure exactly what is being asked.
Your car has Bluetooth, do you want the phone to play is music through the cars radio?
You say the Blaze has music connected to it, no it doesn't, the Blaze gets connected to the phone as an I.put device, as if it was a controller like a keyboard or mouse..
If you don't want to control the Music with your watch, then you should be able to disconnect the BT Classic from the phone, either by turning the BT Classic off through the Blaze settings, our disconnect it through the phone's settings.
Your car is being used as both an input device, and an output device to play the Music.
The Music should play through the car with or without the blaze connected, however with both connected, which has control of the Music can be questionable.