Is this acceptable for a professional paint correction and ceramic coating?..

I picked up my new BRZ last week and complained about the poor condition of the paint. Dealership agreed to split the cost of a paint correction and ceramic coating by their preferred vendor, and I'm not thrilled with the results. There's still a lot of swirls buried in beneath the coating, and it's obvious that a few spots were missed in the coating process.

They offered to bring it back to the same shop to "make it right", but I'm not sure I can trust these guys anymore... What's the move? Is it safe (for a different shop) to remove the ceramic coating before polishing and trying again?