First thing to do is to disconnect the charger from the battery until the problem is resolved.
The battery should be checked, not only may it have a faulty cell, the fact it has become so hot that may have damaged it or at least make it loose electrolyte.
If the battery is faulty, then as its "new" you should talk to your supplier about getting it replased under warranty.
If the battery has survived then it does point to the charger.
However, you have already identified the charger does malfunction, so regardless of the battery's condition the charger needs attending to. I note it is a 1998 caravan and charger technology has moved on since then. You will probably struggle to find an exact replacement, but it should be possible to integrate more modern chargers - if your not sure about how to do it, you will need to use a qualified caravan technician. There are mobile technicians who might be a good bet.
Temporarily you could use a multistage battery charger (Like a Ctek or similar makes) to keep the battery charged I know that Ctek do a 10A model but it is quite expensive, but its good.