I can't imagine the watch and the car problem are related.
The control systems in the car are all hard wired, the bluetooth power in the watch is not going to be anywhere near strong enough to interfere with the car's primary systems. I can't see any electromagnetic radiation emanating from the watch could be strong enough to disrupt systems that normally operate in what is a very 'dirty' environment.
Had you said you had problems with the phone connectivity or bluetooth audio, maybe.