To use shore power, you have to be plugged in to 120V AC power. If you are, the converter in the trailer should supply DC charging power to the battery and it should allow 120V AC power to get to the AC outlets, the refrigerator, the water heater and the air conditioning.
You will NOT be able to us the air conditioner while primitive camping, unless you are hooked up to a generator capable of supplying at least 2500 Watts. If the battery is disconnected, you will not have DC power in the trailer, which means no lights, water pump, furnace fan, etc.
Shore power WILL NOT lift the trailer top! The charging current it supplies is much too low for that task. You need a healthy battery for that high Amp task, which requires about 50-55 Amps, I believe.
If your battery is not charging when plugged into shore power, you probably have a converter fault. It could easily be that one or both of the "hidden" 30 Amp fuses in the converter has blown. This thread talks about that problem: https://www.hilotrailerforum.com/f28...g-repair-6454/