How do I keep my headphone jack from disabling my bluetooth speakerphone in my car? I just upgraded to the Samsung Galaxy S III running Android 4.0.4 (Ice Cream Sandwich) and I drive a 2009 Mazda 5 with integrated bluetooth speakerphone.

When I'm in my car, I connect the headphone jack to my car stereo Aux input so that I can play music from my phone through my car speakers.  I got a phone call today and I noticed that when I'm connected to the Aux jack, my phone wouldn't connect to the bluetooth speakerphone.  In fact, I couldn't hear the phone call at all, although the person on the other end could hear me.  When I pulled out the cable from my phone's headphone jack, the bluetooth connection to the speakerphone was restored.

I never had this problem with my Bionic.

How do I make my phone connect to the bluetooth speakerphone even when I have a cable in the headphone receptacle?

Note: my car hooks up to the bluetooth speakerphone only -- it doesn't have an option to play music through the car speakers via bluetooth.

UPDATE (JUL 19)

Having thought about the situation some more, here's what I think is happening: 

When I make a phone call using my car's integrated bluetooth speakerphone, my car turns off the stereo input to my speakers and replaces it with the phone input.  At the same time, if I have a cable plugged into my headphone jack on my phone, my phone assumes that I want to hear the call through my "headphones" and not any attached bluetooth device, so my phone doesn't transmit the incoming phone audio to the bluetooth antenna -- it sends it to the audio cable plugged into the headphone jack.  Since my car stereo isn't accepting auxiliary input during a phone call, I hear nothing.

So, I really need a way to tell my phone that when I have a bluetooth speakerphone connected and "headphones" connected, I prefer to hear the call through the bluetooth connection (I don't think it's very likely that I'm going to be able to get Mazda to change their stereo firmware :-) ).

UPDATE (JUL 24)


I tried my wife's Razr (running ICS) and didn't have this problem, so it seems to be Samsung Galaxy SIII problem, not an ICS problem.
I've come up with a couple of work-arounds that I'll submit as a separate answer.
From the Samsung tech support, they say that:


  when the AUX cable is plugged in, Blue-tooth audio is dead.


However, from the ICS Options during a call:


  During a call, you can also use buttons near the bottom of the screen to:
  
  
  Switch to the dialer, for example to enter a code.
  Controls the audio output as follows: 
  
  
  If a Bluetooth headset is not connected: Turns the speakerphone on or off.
  If a Bluetooth headset is connected: Functions as a 3-way switch between the built-in earpiece, the speakerphone, and the headset. The icon changes to indicate the current output. Touch &amp; hold to see a 3-way menu.
  If a wired headset is plugged into the phone, it replaces the phone's built-in earpiece.
  
  


Note:
The Google Support link refers to the Android 4.0 for Galaxy Nexus (Released 2011, November), but the one you have is newer (Released 2012, May). Since the OS is the same, there's no reason as to not have those options available.



You can try and check if the mentioned option at point 2.2. works, but besides from that, I believe that you're out of luck on this subject.