76lxhatch

A small trickle charger shouldn't present you with any problems using it this way. You can get the small ones that are basically just a DC adapter and plug into the cigarette lighter socket too - relatively easy and compact. One of these small ones wouldn't keep up with any significant drain of course but might provide just enough charge to avoid problems.

Given the rate of drain that you seem to be experiencing though I'd venture to suggest two other options. Firstly perhaps you need a bigger battery if it never lasts long? Secondly with the caravan park thing it might be simpler just to set it up so that your 240V gear can run from the external power instead of the battery and inverter to save draining it.

Edit - the caravan equipment doesn't usually use a standard plug and requires some sort of electrical cert. A competent auto sparky or mobile home place should be able to help you with this but there will most likely be some cost involved.