I would get a second opinion.. Only the SUV with rear air has 2 cores..
How many people here have had an evaporator leak?
Ask to show you where it is leaking and take pictures.
P050D, rough idle on cold start.. Scan tool misfire data will show the cylinders that are misfiring.. It will only occur during a cold start.. Your not going to see anything on a test drive..
Fuel injectors are the most common failure.. Coolant leaking into a cylinder from a bad cylinder head casting is possible but not common.
Make sure GM customer care is always involved with your concerns.. The dealer is not going to do anything that GM won't pay for.. Getting payment for warranty repairs is not automatic..
The dealership is a business just like any other.. Maximizing profits and minimizing costs..
If GM won't pay for the repairs then it comes out of the dealer profits..
Always get the General involved because the General pays for the repairs not the dealer.
Did you try unhooking the neg. Cable for a couple of minutes to do a reset.? Make sure that the new battery is fully charged.. Sounds like a low voltage issue.