Bluetooth RCA patch?

The problem:
Having a big and bulky phone (cursed smart phones), it is hard to dig out of my pocket in time to answer any incoming call while in the seated position IE in a car and driving.

The solution:
Bluetooth RCA patch board. Luckily enough for me, my car already has an amp powering all of my speakers.

Next problem:
None exist to my knowledge. I had hacked a Bluetooth shower speaker, and this kind of worked, but it was clumsy and was either the radio or Bluetooth. I say had hacked because the cassette deck that it patched into died. I opened that up and the whole mechanism was toast.

What I would like to do is create a patch board that under normal circumstances, acts as if its not there, but still connects to my phone. But when I get an incoming call, my phone yells directions at me or I decide to play music from my phone, it stops the radio signals, and sends the phone audio to the amp, and then to the speakers.

Would this actually be feasible to achieve, or am I chasing an illusion?

I would also like to be able to pass voice from a mic located in the car through this for phone calls.

Have you ever considered buying a car stereo with bluetooth built in as this would probably be the best option in the end.