Transmission fluid or oil in radiator?

[Ranger1993]

Gents, I am confused. I'm no mechanic (I change my oil and air filter though!) so I'll need help on this one.
Several months back noticed about a teaspoon of red fluid on driveway.
I have transmission fluid loss. I was at a red light a month or so ago and went to go and there was a few seconds delay before it kicked in gear. I have been checking the T fluid level and adding Rislone ATF with built in stop leak.

I was checking the overflow radiator bottle and noticed the fluid was blackish brown. The inside overflow black rubber tube was swollen and like a jelly. The radiator fluid was very oily with a clearish slime to it. I haven't lost in radiator fluid and the vehicle does not overheat.
The teaspoon size puddle under the truck is like an lightish oil color now.

Checking the oil dipstick it shows NO foam, its clear and full, no oil loss.
The transmission oil is clear, but I have to keep topping it off.
I took the truck in to my mechanic and he said it is motor oil getting in the radiator.

Said try Blue Devil, that it could be a head gasket or cracked block.
I've checked other auto forums, and people insist its not motor oil but a cracked transmission cooler in the radiator, that one should replace the radiator.

Any thoughts on this? I really don't think it is motor oil, as I said, dipstick shows no oil loss and is very clear.

[Stealthee]

Replace the rad. Your mechanic isn't a good mechanic if he is insisting its oil, and for suggesting something like Blue Devil.

[Ranger1993]

Thanks Steelthee for getting back to me.

What really upset me was the jelly like rubber hose that was floating in the overflow bottle.

I do have a transmission leak, seeing about less than a teaspoon a day on the driveway. But no "strawberry milk" at all in the overflow bottle.

Can overheating cause the radiator fluid to become really greasy and turn the internal overflow hose to jelly?

I've included some photos of inside the radiator. Let me know what you think.

https://ibb.co/J5ckZxk

https://ibb.co/NL7j6m1

https://ibb.co/q0zS58W