I would try then a higher quality DAC (Digital to Analog Converter) than the little dongle Apple provides.
You can get on Amazon iSimple Dashboard Mounting Kit for Apple iPhone Device with Lighting Cable for example, or search online for a higher quality product. Apple's goal here was to make a descent DAC but as small as possible, perhaps a larger module specifically designed for audio out (instead of headphone out) would work better in the car's environment.
If that doesn't help you can always return it for a refund.
Another option is to get a Bluetooth car audio adapter, plenty of those around.
Otherwise
Take your iPhone and headphone adapter to an Apple store or other Apple authorised service location to have this issue diagnosed.
Or contact Apple support: https://support.apple.com/HT201232