We seem to be going in circles a bit here, and it’s entirely impossible for the experienced mechanics here to come to a concrete determination without being to inspect the engine and turbo in question. But let me restate what I think…
When your turbo failed the first time it was a symptom of a failed engine. Yes, I agree that the shop was sloppy or did a rush job by not searching for or addressing the sludge issue that caused the turbo failure. However, despite other responses you’ve had above, once there is enough sludge to cause turbo failure, the engine is done for. There is no amount of scraping, cleaning, flushing, or whatever, that can reliably and completely remove that kind of sludge from an engine.
Bottom line, your car needed an engine when the first turbo failed. No matter if you replace the turbo oil feed and return lines and clean the oil pan and valve covers and PCV system, there is still sludge on all the internal surfaces of the engine that can not be removed without entire engine removal and disassembly.
Your wife should have been sold an engine and a turbo at the first visit. Or alternately given the option of spending a couple hundred dollars labor to investigate if there was a sludge problem. But assuming that the engine was sludged up 12K miles ago, the issue now is that you were not sold an engine–or told that you needed an engine–at the first visit.
What are you looking for in reparations from the dealer?
It sounds as if you’ve already walked away from the car, is that right? That would make the car a total loss for you. The cost, at a local independent shop, to replace the engine with a good used one, should be far less than what you could sell the car for on the open market. A clean, straight, well-maintained 4-5 year old car is a great candidate for used engine transplant, then giving you more service from the car or several thousand dollars from a sale.