Seems that this is a classic case of poor (or very little) preparation by the dealer prior to application of the ceramic coating, so Williams are probably correct in directing you towards the dealer. Preparation is key, which should have included a full decontamination of the bodywork before the coating was applied which, depending upon the condition of the paintwork, would consist of some or all of;
- iron fall out removal
- tar removal
- claying
- 'correcting' any defects in the paint - scratches and / or swirls
Even on a new car, there can be a surprising amount of contaminants on the paintwork - picked up during storage and transit from the factory to the dealer/customer, and applying a sealant / coating to a washed car without adequate decontamination prep will produce the results you are experiencing on your car. The
problem with dealers applying any form of paint protection is they are rarely adequately trained or allocate sufficient time to apply these coatings. Hindsight is a wonderful thing, but it's much better to pay a professional detailer to the job, or if you feel confident and have the time, products and equipment, do it yourself.
If it was me, I'd speak to the dealer and ask them to explain the process(es) used in applying the coating. This should highlight whether or not they applied it to 'dirty' paintwork. It does sound as if it needs to be re-done. If you paid for this (usually not cheap!) rather than the dealer having included it 'free' as part of the deal, then I'd be asking for my money back, and getting it rectified professionally. Under no circumstances would I be letting the dealer re-do it!
Good luck. Hope you get it sorted.