Royce, please PM me. I do this stuff for a living. After we get it worked out, will post back here.

An Inverter takes battery DC voltage and makes it into 120 VAC "house current." Many nice inverters have automatic battery chargers with transfer switches built in...when you plug 'em into the AC outlet at your campsite, they start charging your battery, while still keeping all your stuff running.
You likely have some things running at 12 VDC right off the battery, and other things running at 120VAC off the inverter, which is getting power from the battery.

In any case-- 3-4 years is about the normal battery lifespan on a small system. At my house, the battery bank weighs over a ton, and cost $2 grand. It will likely last about 8-10 years. With a tiny battery bank in your camper.....if you use more than you charge, or you let it sit all winter with nothing coming in (very bad) -- 2-3 years is about right.Depends on the size of the battery bank.

Let me know if I can help. Come to Lowell, and I'll fix it on the spot <grin>

DANBOB