2002 Monte Carlo transmission/radiator

It appears I have transmission fluid leaking into my cooling system. I noticed a leak and it was not water. I also noticed my coolant tank was way too full and that I was low on transmission fluid. I dumped some of the coolant and then refilled the trans fluid. All was great for a few days. Then a major leak again. My coolant tank is full again and the trans fluid is all but gone.
Do I need to replace the radiator, or just the cooler? Is the cooler attached to the radiator? I am an intermediate mechanic, but am not familiar with this newer cars system.