2000 Mazda Protege overheating

What we believe happened is our vehicle overheated and smoke was coming out under the hood. The dealership said we blew the engine and would need to replace the engine. We found an auto shop who replaced the engine with a used one with 34K miles. About 200 miles later after picking the car up, the car overheated on the freeway and had to be towed back to the shop. The owner said the problem was an alternator and water pump and a missing belt, so we had him fix that. About 150 more miles after that was fixed, again the vehicle overheated on the freeway, and again towed back to the shop. This time he says it's the head gasket, and is saying it'll cost another $600. He says it is not the engine nor anything to do with the replaced engine. My question is could the head gasket have been damaged as a result of a bad engine? Or is it something totally unrelated? If we fix the head gasket, what else could go wrong with the engine and/or cooling system that would not have anything to do with the engine. We feel we are throwing money at this shop dealer, and he isn't really fixing the problem.