Hi,
I would not disconnect anything. Shut off the propane leak detector, so it will not draw to much power from the battery. The 95 watt solar panel will not keep up well with the current draw, so if you can leave it plugged in, that would be fine. The battery will not "Boil dry" as you might think, it will be fine for 2-3 months, just a little low on water when you get back if it has been really hot.
If you have a Fantastic fan, then it's 2.5 amp draw will deplete the battery, and leaving it plugged into shore power all the time will avoid the battery going up and down in voltage, saving some water.
The solar charge controller will see that the battery is at around 13.2 volts, and probably will not turn on. If it does turn on, then the charger will see the battery at 13.4 volts, and stop charging until needed. You can safely leave both connected, they will each do what they need to do, without damaging anything.
Fred.