Determining ethernet wire category/speed

This is most likely a problem with the cabling at some point. Here are the most common problems I have found to cause this in my experience (without certified test results on the installation, which I presume you do not have):

• Improper termination of the cable to the jack/plug.
• Physical problem with the cabling, often the result of the cable being pulled too hard during installation.
• Physical problem with the jacks or plug. This may be a manufacturing defect or the result of improper testing (I have often seen the pins in a jack bent when subject to the "probe" when toned out).
• One of the network cables you are using to connect the computer to the wall could have a problem (this is far more likely if the cable is hand made or older).
• Every once in a while you may come across a network cable that only has two pairs. They were sometimes manufactured this way because it was cheaper to do so.

While 10-BaseT and 100-BaseTX use only two pairs, 1000-BaseT uses all four of the pairs found in your standard Cat5e or higher cabling. If any one of the eight wires has a fault of some sort, this will prevent your connection from negotiating to 1000-BaseT and result in a 100-BaseTX connection.

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 answer 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 you do no have power and are running one or more laptops on battery, then consider these cheap pre-made plugs over building your own cable. Keeping things standard is a good thing.