There is no reason to do what you're trying to do. Just get one of these. Easy peasey.
Amazon.com: Anytime Tools 7 Way Round to 4 Way Pin Flat Blade Trailer Light Adapter Plug Connector RV Boat: Automotive
I think the piece at the bottom of the picture is actually the trailer brakes adaptor. I could be wrong though.
Disclaimer -- This is assuming you have the full trailer tow package and your trailer is already wired and all your trying to do is plug your trailer into the car so your trailer lights work. That is what I think you are asking about.