Welcome to LOC!
That is strange...I have the 3gs and have no problems like that. I also pair my Ipad so my kids can watch movies as well. I still have my phone paired and take calls, it will mute the ipad audio and as soon as I hand up the ipad audio will start back.
You have the phone paired under phones and also the MP3 player paired in the audio...right? One thing to try may be to start over...remove the phone from your RX350 and start all over...and see if it still does it. It shouldn't make you shut the car off everytime.
Good Luck!