OK, riverdawg. First, the "non-GFI outlet" is REALLY GFI protected. It's part of the circuit that one of the GFI outlets protects.
Second, if the GFI outlets will not reset, you have an "open ground", which the GFI's protect against. So, somehow, the grounding wire in your shore power input is possibly broken, or does not make good contact where it's connected, or your home circuit has an open ground.
In my trailer, the GROUND wire is behind the converter and it's a bare copper wire. Don't confuse it with the white neutral wire. That wire should provide a complete circuit back to the ground wire at your home outlet. If it does, then you MAY have an open ground in your house wiring. If that outlet is not GFI protected, then you would have power there, but it would trip the GFI's in the trailer. And, you would have a potential shock hazard using that home outlet.
The GFIs WILL reset if not powered, but as soon as non-grounded power is sent to them, they will trip again. You can use a simple receptacle tester, like this one:
https://www.homedepot.com/p/Power-Ge...-oUchRcdpOVmWk
to check for correct circuit wiring, both in your trailer and in your home.
Your trailer battery is connected fine and is good, since you can raise the top, and the lights and water pump work. If you test the terminals with a multimeter and you get above 13 Volts with shore power connected, your battery is also being charged by the converter. I suspect that is the case, since an open ground will not prevent the converter from transforming AC power to 12V DC for battery charging.
- Jack