Weird Bluetooth Connectivity Problem
 

I have a 2011 A4 and my wife has a 2016 Q5. Both of our cars paired just fine with our old iPhones, but a few weeks ago we upgraded to iPhone 7s, running the latest iOS. Here's where it gets interesting. My phone pairs and works just fine in both cars (and how nice to see Audi finally lets us stream audio over Bluetooth...I still can't believe my car doesn't do that!)

But my wife's phone won't pair with her car, no matter what we do. One time we got as far as the "Does this code match the one on the phone" screen, but it still failed. Every other attempt, the car cannot find the phone and the phone doesn't show the car as an available Bluetooth device. Again, though, her car finds and connects to my phone just fine (which would seem to eliminate the Q5 as the culprit), but her phone pairs and connects to my car (and other Bluetooth accessories), which seems to rule out the phone as the problem!

I've tried resetting the phone, erasing all the paired devices from the car, but nothing seems to work. I'm happy to seek professional assistance, but I don't know whether to go to the Apple Store or my Audi dealer!