Black coolant in the plastic jug?

Yep, this happens when the transmission oil cooler goes bad, here is the location so you can swap it out, you will need to flush the cooling system using a chemical flush you can get from the auto parts store. Check to see if the transmission fluid is dark as well to help confirm the issue. Also, this guide can help:

https://www.2carpros.com/articles/transmission-fluid-in-radiator-coolant-reservoir

You will need to replace the radiator if the fluid color is confirmed. Please upload pictures or videos in your response of any problems so we can see what to help you with.

The cooler is inside the radiator, please go over the guide above. It could be a blown head gasket as well, since there is oil pressure going through the head gasket. I need you to see what color the transmission fluid is. If it is red and normal, my guess is that the head gasket is bad.