Re: two wire trim swap w/three wire
Your remote control is irrelevant, and can be used. Here is a better picture of your current set up, before the modification you want to do.
Simply cut and disconnect the 2 ground wires, and ground the black wire from the trim motor to ground, as per the first set of diagrams provided. Now when there is no power to the relay, there is no connection, and when there is power, you are getting 12V, which will either raise or lower your motor, depending on the button being activated. In my second original diagram, imagine that the 3 wires coming up from the bottom of the page are coming from the trim motor.