Music drops/stutters intermittently when iPhone is connected to car stero over bluetooth

My family has three cars and we all typically connect our iPhones to their stereo via bluetooth. We are experiencing a phenomenon in which music that is being streamed from the phone to the stereo abruptly stutters and/or drops momentarily and I'm trying to prevent that from happening (short of plugging the phone into the car via cable).

I've noticed that this phenomenon happens when another car is nearby, be it in heavy traffic or driving on a freeway with a car next to me one lane over.

What I have discovered is that when the stuttering/dropping happens, our phones have connected momentarily to a foreign device in another car nearby (see the three attached images). All of the documentation says to press the (i) and select forget device but that doesn't work because 1) there is no (i) next to these strange devices and they are not selectable and 2) I cant possibly forget every other device in the world as we get near them in my automobile.

How do I stop my phone from connecting to other devices automatically and/or how do I get the stereo to stop stuttering as my phone connects to these foreign devices?