OK, I have a clearer picture.
So first, let's talk about battery charging. You batteries are charging when you plug into shore power and your converter (GPC-30) is on. I believe the "charge" switch that you're referring to is used to turn on and off the converter. So, the first thing you should know is that your battery charger is a single-stage charger. Modern chargers use a three-stage technique and can be left to charge the batteries indefinitely, while the single stage chargers can overcharge and damage the batteries. I don't know if your batteries are permanently damaged, more about that later, but when you are connected to shore power and your converter is on, it's important to not overcharge your batteries. Folks often will swap out their old single stage converters for a modern three-stage converter. The new converters cost approximately $200 and can be done by someone with basic electrical skills or you can find a RV tech to install it.
When the previous owner said there's no 110 V, I think he was saying that even when you are connected to shore power, you don't have 110 V available inside the trailer. You can always upgrade your trailer to include an inverter. An inverter converts 12 V DC into 120 V AC. Depending on the configuration you can add 120 V wall sockets powered from your inverter. Some inverters come with automatic switchover circuitry which means that your 120 V wall sockets, when connected to shore power, will receive their power externally, rather than using your 12 V batteries as a source of power.
So, I guess your first problem to solve is to see if your converter is charging your batteries and if your batteries are healthy. Can you measure the voltage across each battery BEFORE connecting shore power? Can you repeat the measurement across each battery AFTER connecting shore power? Make sure the switch is in the charge position when you connect shore power. This will give us some clues. A good way to check the state of the battery is to buy a battery hydrometer. You can pick up a cheap one from Walmart and it will give you and us a clear picture of the health of your batteries.
2015 30' Classic, "Chez Nu"
2014 RAM 2500 w/Cummins Diesel
ProPride Hitch, 400 W Solar