Guess I'm a bit confused on battery reading FULL then 1/3 full. What meter is giving you these readings? Do you have a gauge built into the trailer?
Are you saying when you first plugged it into the house power, a meter showed it going to a high voltage reading, and then a few hours later dropping down to a lower voltage reading? If so, that might be normal; depends on your converter.
I know on my trailer with a WFCO, if the battery is 50 percent low (or lower) on charge, it will boost up to 14.4 volts for about 4 hours, then drop down to 13.6 volts, and eventually, drop down to 13.2 volts for a float mode.
Battery stored in garage over winter, low on fluid, if weather got cold enough and battery was not charged, it could have frozen.
You can use a standard volt/ohmmeter (aka Multi-meter) but make sure it is on the VOLT meter setting; do not check when on the ohmmeter setting or you will blow a fuse or kill the meter.
This chart gives an idea of how charged the battery is at certain voltage levels.