My 04 Escape, V6 4WD, has tranny fluid coming into the radiator reservior up through the smaller bottom hose. I would have to think that anti-freeze is going into the transmission. My guess is an internal break inside the radiator. I'm thinking of going with an external trans cooler and plugging the lines coming out of the radiator. Will have someone flush the tranny and I'll flush the radiator. I suspect the anti-freeze would act the same as water in the trans and cause it to eventually lock up. Tranny fluid in the coolant I have no ideas what that would do, maybe eat the rubber on those hoses? Anyone put a tranny cooler on this vehicle and have any tips to avoid any mistakes?

I would suggest you stop at a radiator shop and get a new cooler in the radiator. Then check transmission fluid for anti freeze and flush cooling system.