Dan,
You idea is wrong from the start.
You need the inverter as close to the house bank as you can possibly get it, but still have it be in a protected place and not exposed to the battery acid vapor. It does not matter where it ends up because the 12V current is 10 times the 120V current. The 120V you can run in a household extension cord to the other end of the trailer with very little loss.
You won't ever fish wires (particularly the size you need) though the laminated walls of a modern trailer. But you can get surface wire mold at any big box and put the 120V cord in that. When I quote internal wiring and surface wiring in an RV, they always pick the surface way. Funny thing.
We did a lot of boat work before the depression and I ran into this a lot. The problem was always the same and the fix was always the same.
Matt
