Ethlene Glycol (antifreeze) will ruin the clutches.
I have a 2002 Truck and noticed today that the radiator overflow was leaking all over. I thought the worst " head Gasket". What has actually happened is leaving the transmission entering the bottom of the radiator is a line it then exits from the top of the radiator and enters the external transmission cooler and then back to the transmission. Inside the radiator there must be a crack since the transmission fluid is mixing with the radiator fluid. I am somewhat relieved, but also confused as to why they are using the radiator in the first place? I want to disconnect and plug the lines to the radiator and have the lines go direct to the cooler and back. I do not know if I can do that or not?
You must get as much of the mix out of your trans and related components as possible or your clutches will go.
Drain the trans, change both
the internal filter and the spin on, wipe out the pan with a clean lint free cloth. Then do what they refer to as the 'hoot' method for getting most of the fluid out of the lines and torque converter. For your situation, count on using in the neighborhood of at least 20 qts of ATF. Cheaper than a new trans. You might even consider doing the 'hoot' a second time after you have driven the vehicle a few miles.
This just happened to a friends Mercedes, same issue, but it wasn't caught in time, had to have the trans completely rebuilt, including all new internal electronics.
The radiator is used as a pre-cooler in summer and a heater in the winter.
A good radiator shop can replace the end cap of the radiator that contains the trans cooler. This is not something you want to let slide. Good luck.