Ok, I traced some wires this morning and I have a better understanding of a couple of things. Sorry the pics are so bad, my phone and the dark don't mix.
The picture above is the back of my inverter. The plug in the top right corner is marked AC Input and the wire comes from the outlet box that is in turn wired to the shore power outlet (inlet?). Unhooking that plug should prevent the inverter from trying to charge off shore power, I think. The wires on the left run to the main battery cutoff switch. Those will stay, so the inverter can draw from the battery to power the outlets on the front of the inverter as well as the external outlet on the trailer.
This is the front of the inverter. The cord you see runs down to the external trailer power outlet I mentioned above. So that stays in place.
I will need to mount the new charger, someplace I can see the indicators, run wire from the shore power to the charger, and leads from the charger to the battery.
This is the external power outlet. The larger cable runs to the shore power connector. The smaller two run to the front and back of the inverter, as described above.
From tracing wires from here I've determined that three things are connected directly to the bank.
The largest wires go to the main battery cutoff switch, the big round black object top left. That in turn runs the switches for the lights, water pump, and unused aux. connections.
The smaller wires go to the solar controller, which then connects to the panel. Which leads me to believe that the solar connects directly to the bank, regulated by the controller, all the time and regardless of the setting of the main battery cutoff switch.
The last thing connected directly to the bank is a wire that goes into the main compartment for a tiny LED compartment light. Basically so I can rummage around without unlocking the electrical compartment. It was clearly an afterthought.
Ok technically there is a fourth thing directly off the bank. The negative terminal is grounded.
All the positive wires connect to the positive stud on the first battery. A heavy gauge wire, maybe a 2 or 4, runs from the first battery's negative terminal to the second battery's positive terminal. The negative and ground wires connect to the second battery's negative terminal.
Just for entertainment, here's a picture of our overall setup, full battle-rattle.
Just the trailer...
And a gratuitous shot from a campground near Moab.
(ETA: I mentioned this was a prototype...Originally the product line was going to be called Basecamp, but then they realized that there are multiple product lines called Base Camp or some variation...so they changed to Borderland before they went into production. The prototype was later auctioned off for a Boy Scout fundraiser. I bought it from the auction winner for a fraction of what the production models sell for...They look amazing but I'm putting two kids through college here).