'96 Taurus Transmission Fluid & Antifreeze question

I have a 1996 Taurus w/3.0L OHV engine> I bought this car with problems. After a test drive around the block a couple of times I pulled the car back into my shop when I opened the hood I was getting
overflow from the cooling system with transmission fluid in it. I had just filled the cooling system & was testing it out. It seems the transmission oil cooler sprung a leak. I'm in the process of putting in a new radiator. After the radiator install I want to drain & change the trans fluid. I don't think much if any coolant got into it. The cooling system had mostly water in it because it needed flushing. the trans fluid is pinkish rather than red. I plan on draining the transmission pan then fill the trans fluid, drive around the block a couple of times then drain it & refill again.
Any ideas/experiences with this? Is there a way to drain the torque converter to do a better job on this?
TIA Frank

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