I tried the Dot in my car, tethered to my iPhone, but the results for me were sketchy at best.
I had the Dot powered by a USB port, and the Dot plugged in via Aux to the CarPlay Stereo.
I couldn't get the in car display to show anything from the Dot.
I now just have Alexa using the iPhone only.
The iPhone is now connected via Bluetooth to the Car stereo (instead of hard wired into the car's USB socket), and I have the Amazon Music app on the iPhone which I play music from, and whenever I want to use Alexa, i Press the Alexa button on the iPhone, the music stops & I say what I want done. (The iPhone is in a BRODIT Cradle to the right side of my Steering wheel, so no looking away from the road).
The music that is playing within the Amazon Music App, is shown on my In Car system (though, NOT CarPlay).
I can still use Siri hands free to make/receive calls etc.
Seems to work ok for me.