I'm just farting in the wind here... ha, ha.. I don't know much about this either, but can't you have a battery disconnect switch to the trailer's 12 v system, then wire the 2k watt invertor directly to the battery and then plug your shore power to it and then essentially be the same as hooking it up to a generator? Then get a second battery disconnect for the 2k watt invertor and switch beteen the 2 as needed?
With the trailers battery essentially 'offline' in the system, everything will be running off of your battery connected 2k watt invertor, even the 12v systems..
You might lose some watts in the transfer with the 30amp shore power plug and dog bone connection, but, when I use the battery disconnect on my TT and then plug in the shore power, everything still works, 120v and 12v stuff. Just not charging the batteries.
Dunno... Good luck! Mitch