I am trying to wire two Ethernet jack ports into a trailer outback so two computers can plug into the wall at the same time. I have one long CAT6 cable with an rj45 connector on one end that is plugged into the router in the main house, and loose wires on the other end.
OK.
Do I need to wire two jacks into the other side of this one cable and plug it into two ports in the router?
Short answer: yes.
Longer answer:
CAT6 (and cat 5 and ..) cables have 8 wires. 4 of those for 10/100Mbit Ethernet. All eight are used for gigabit speeds.
This means that you can split one 8 wire cable into two sets on both ends and run two 100mbit connections over it. You can do this either by creative wiring both ends, or you can use existing plugs similar to these:
This will effectively wire your network like this:
This is likely not officially supported, but it works well enough.
Note that you cannot run gigabit speeds over these cables anymore. YOu no longer have the 8 wires per connection needed for that.
If you have any electrical power in the trailer (and I presume you do, if for nothing than to run the computers off), then the proper ansewr becomes a 'do not do this, but a switch instead'. 4 port switches are dirt cheap, do not limit your speed down to 100Mbit and will save you a lot of time.
If youdo nto have power and are running one or more laptops on battery, then consider these cheap premade plugs over building your own cable. Keeping things standard is a good thing.