Transmission and coolant mixed

It is good that you understand the need to get the coolant out of the transmission. Rather than doing repeated fluid changes, this is one time I would prefer a transmission flush. That is supposed to get all of the old fluid out, including what is trapped in the torque converter, clutch packs, and passages.

After three fluid changes, I suspect any coolant left in the system is going to be rather insignificant. I am sure you drained and refilled the coolant already. Engine oil or transmission fluid in it will deteriorate the rubber radiator and heater hoses.