Hi
The color codes on the cables going to the 7 pin adapters are not always "standard".
The ground wire from the 7 pin already goes to the trailer ground. It needs to stay there / no benefit to moving it. Just wire the ground for the input and output. of the converter to the trailer chassis ground.
The "hot" wire from the 7 pin goes to an auto-reset breaker. That breaker attaches to the main
12V bus bar. Typically this "stuff" is up in the front of the trailer somewhere. All you need to do is move that wire from the breaker to the DC/DC input.
At that point you will have all 18A trying to run from your TV to the battery.
The gotcha is that a lot of vehicles can't supply that much current to the 7 pin connector. Without knowing what the TV is in this case, there's no way to guess at that part.
Just for reference: No, you won't fry your alternator without the DC/DC. That information is talking about a van installation with giant cables running to the alternator. This is *very* different than what you are doing.
Fun !!!
Bob