I'm building a trailer with 110v and 12v. I have a WFCO converter that is wired to my shore power inlet, my 12v lines, and my deep cycle battery. As-is, the system is working great when I'm connected to shore power (I get 110v, 12v, and the battery charges), good when I'm disconnected from shore power (12v works), but I also need 110v when I'm not connected to shore power - so I bought an inverter.
My question is - how do I connect the inverter to the system so that I can "seamlessly" go from shore to non-shore. If I try and connect it into the existing setup I get issues (GFCI and reverse current) that I'm seeing with the testers I have. Is there some type of diode that I need to put in the circuit? Sorry, I'm a beginner to this stuff - but no shocks so far

Thanks, Art