D@mn man, sorry to hear about your luck with an incompetent dealer.
First, on the financial end, prepare yourself to hopefully not get screwed for a very expensive potentially unnecessary repair. Hope you haven't settled up on the first repair yet, I'd gather facts and go to the GM of the dealership before paying up. Guess I'm saying, have a strategy based on what information you can get because the stealer has one to stick you with the bill.
Yes a comp test would reveal a blown hg, or cracked head/block. Just wouldn't know which until opening it up. HG is the most likely problem though.
Define puking coolant. Burning it, turning the oil milky (horrible for you hpop by the way) leaking into cooling system, or physically leaking from where.
Could be something just not reassembled correctly if it's leaking on the ground.
New comp test will tell if it's fixed internally on that side.
Ahh this is going to be a long post......and it will ramble being a one way conversation.
Ck your pm box. I'm going to pm you.