Ron,
There are some problems with doing things the way you suggest.
First, you do not want the wire that supplies DC power to the refrigerator to be controlled by the ignition or else your refrigerator will run only when you have the ignition on. Unless you drive a lot more than you park, your food will spoil. Most RV refrigerators use AC electricity or LP gas to cool, but they require DC power to control the system.
Second, you mentioned that you were going to control a relay. In this case, all you need is a signal to the relay to close when the ignition is on. You do not need a large wire. A common source for an ignition on signal is the cigar lighter wire, or its fuse at the fuse panel.
Third, the actual power wire to the camper should be large enough to carry the load. It should come directly from the battery, or an equivalent. The hot (battery charging) wire that is at terminal 4 on a factory trailer plug should work if you don't want to install a new wire.
Good luck,
Loren