This is a huge job. I suggest taking it to a garage.
As of yesterday, I discovered I have the same problem with the exact same car.
I have bypassed the heater core until I evaluate my options. (You can do that in this part of the country.)
Were you able to effect a repair without paying a Cadillac dealer to do all the work for you ?.
An independent repair shop charged me $340.89 for this work. The core was $193.26 (plus tax), the labor was 1.80 hours at $68.50/hour, plus antifreeze.
The work required is not extensive and there is nothing 'huge' about it. You access the climate control housing by detaching the panel under the passenger air-bag and removing the glove box. The heater core can then be removed from inside the car after removing the back panel from the climate control housing. I had to return the car to the shop as the heater was making a howling noise. As it turned out, there was a leak in the join (between the two panels of the climate control housing) which was rectified by applying a small section of special thick tape to the un-taped part of the join.
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