You have left out a few details, but I will try to help anyway.
First of all, Iknow of no Travel Trailer that doesn't rely on a Coach battery to power the interior lights, alarms, 2-way fridge circuit board, temperature control panel and more.
And, this Coach battery is kept charged by your Converter which in turn operates on 110VAC.
Also, your symptoms of the power (I assume the 12-VDC from the Converter) cycling ON and OFF every few seconds is a common symptom of the COACH battery not taking a charge or even not being there, and the Converter not being able to handle the load on it.
If you have a model of travel trailer that is designed without a Coach battery, then I would love to know the maker and model.
Otherwise, find and Check that battery.