Unlikely to be a wiring fault per se. More likely an overall design weakness giving unfavourable interaction between the Audi DAB antenna design and standard car charger design.
I'm thinking rather than the charger outputting EMI or RF and actively interfering with the DAB signal or even causing dirty DC noise in the wire harness, when it's operating under load with a phone attached, it and the cable are more likely behaving like an active antenna and drawing some of whatever signal is available. The signal strength varies with weather too which might explain the times you do have a weak glitchy signal and other times none at all. The signal arrives at the window antenna after making it through the fuzzy ball of the EM field surrounding the car so some of that power is lost already. If some of the remaining power is being picked up by the charger / cable / phone array, then that doesn't leave an awful lot for the DAB decoder to process.
DAB is a fairly weak signal at the best of times and the quarter window antenna (or where it is in cars other than Avant) is not in the best place for great reception. I doubt Brodit will admit to knowing about this to an end user. DAB still has a fairly small adoption in the UK car market so I would guess Brodit know about this but will keep it dark until existing stock of current models have sold out of the warehouses or DAB users increase and it becomes a significant enough problem for them to address properly. Other makers will be doing the same. All of their products will have been tested for EMI radiation and RF interference that can be injurious to health and equipment like pacemakers and the like but not for soaking up low power DAB signals.
That's my slant on it as someone who works for a large corporate professional digital media company.
Admit nothing. If you can't fix it, feature it. If you can't feature it, kill it. If you can't kill it, best admit nothing.
