2003 Hyundai Elantra Repeated Car overheating for years

I purchased a new 2003 Elentra. From the time I got the car I had issues. In the Hot Arizona summer when I would slow down or stop at a light the temp would go up and blow hot air. In the winter it would do the opposite. I would have to repeatedly take it in about 3x a year and the coolant level would always be low. I always had it in under warranty. I have had water pump replaced, a few thermostats, pressure tests done and it continued. The last time I had it in I was told they found a pinhole leak. It seemed to finally be fixed. I am not out of warranty and I had a new issue. I smelled a nad oder and smoke/vapor came from vents. The a/c would still blow cold however. I was still having issues with coolant disappearing. Today I was told that a needed a new heater core. $900 I was told. They said they would try to have hyundai goodwill 1/2 the cost. My question: Could this have been the cause all along, or could my issues have contributed to this failure? I think I should have this replaced for free but I am not confident this will happen. What should I have them test after this replacement? I read about electroysis, I just do not want to pay $900 and find I still have an issue.