reverse gear will not engage when hot

Good morning.

It sounds like you have either a failed seal or drum in the transmission. This is an internal failure.

What did the condition of the fluid look like when you changed it?

Roy

https://www.2carpros.com/articles/automatic-transmission-problems

The transmission fluid was dark.

Here is how to change the transmission out. Check out the diagrams below. Let us know what happens and please upload pictures or videos of the problem.

Cheers, Ken