Your main draws are not the water pump or lights or slide, but most likely the control circuitry for the fridge and the power needed for the propane and CO detectors and so forth. If you're camping somewhere cold and using the furnace, that is a quite significant electric power consumer.
That battery charger should work, but your built-in converter would probably be at least as effective (and probably more so).
It's impossible to give much accurate advice without a better handle on what your actual electrical use is, including the parasitic sorts of drains. That said, I might venture to guestimate that the battery you link to would be good for about a day of camping if fully charged without getting too deeply discharged, but almost certainly not a few days. Even a pair of golf cart batteries would probably be pretty tight for 3-4 days with no charging. A solar setup, even a rather modest one, would be a big help here. ("Rather modest" as in maybe a couple hundred watts, not as in 10-20 watts!)
