1st of all, welcome to the forum.
I tried to look up your trailer, and came up blank. What is the manufacturers name ?? I am not even sure that is a Forest River product.
As far as using the TV with your antennae, the booster does need to be on. Raise the antennae and do a channel search with the TV (in the antennae mode, not cable mode). Rotate the antennae about 1/3 of the way, and do an add channel search. Rotate the antennae the opposite way, and again do an add channel search. If you don't get any channels using that method, then you may not have any OTA channels available in your area.
You outside cable connection should look something like this:
Do not use the booster button when using the cable connection.
Chap , DW Joy, and Fur Baby Sango
2006 Ford F150 Super Cab 4x4
2008 Surveyor 263