In general, there are two different kinds of circuits: parallel and serial.
In the parallel configuration, your incoming single line splits into several parallel lines, each of which has the same voltage as the other lines, and when you put a load on one of the parallel line, the other parallel lines remain at the same voltage. This is basically how your trailer, or any house is wired.
In a serial configuration you have a single line, and as you add loads to that line in "series" (ie., one after the other), you will see a voltage drop across each load, so that your first load sees the incoming 110V, but the second load sees only what is left over after some consumption from the first load.
So what is happening in your system is that between the shore power outlet and the breaker box distributing power (via a parralel circuit) to the outlet inside your trailer, you will effectively have a series circuit. Normally the "loads" in this series circuit are pretty negligible, but something in your system is causing a substantial load that is causing a voltage drop (incidentally, your converter should be on one of the parallel circuit branches, so should have no impact on the other parallel branches).
The absolute first thing I would do if experiencing low voltage inside the trailer is to unplug from the power post and verify that you are really getting 110V at the pole. It is not uncommon for the power posts in campgrounds to deliver lower than standard voltage. Now, if you are getting 68 v inside the trailer, but have 110V at the pole, then you have a "loss" or load in between the power pole and breaker box. Be sure also to check all of your outlets--make sure you are seeing the same voltage on all of your parallel circuits.
An obvious culprit (potential load in the series circuit) could be your shore power lead. If you were parked too far from the power post and had to use an extension that was about the same length as your basic power lead, you just doubled the resistance (load) in that part of the series circuit. This could be further aggravated if the lead or the extension are of too narrow gauge of wire, if there is corrosion on any of the male of female contacts on the extension, or corrosion in some connection inside the trailer. If you are handy with a Volt-Ohm meter, you can trace the circuit from shore power plug to breaker box, and you ought to be able to identify which compoenent is causing the drop. If you want to try something a little more quick and dirty, try just putting a hand on any (insulated) connection you can reach and see if it is warming up (don't grab any bare conductors).