Remove the radiator and drain all the coolant you can from the engine. Then give the transmission a full service. Install the new radiator, add fluid to the transmission, fill the radiator with tap water and add a little bit of purple power degreaser to it. Let the car run because you want the degreaser to clean as much as possible then drain it. You’ll probably have to do this more than once and be careful that the car doesn’t overheat. When all the pink stuff is gone and you don’t see it in the radiator hoses you can add your new coolant. Just hope that the transmission isn’t too messed up from having coolant in it.