Can't see how it could be any of a,B or c because the display is showing around 13v in the leisure battery with that increasing when on EHU.
That means the battery is decent and must be connected to the PDU.
Draw it out and you'll see what I mean.
I suspect the OP actually has NO 12v system output whatsoever whether on EHU or not ( 12v fuse/ fuses/ main isolator issue?? ) and the equipment he sees working on EHU is all 240v.
There's only one way the OP can have a12v system that works on EHU only is to have no leisure battery connected to the system (so the battery charger works as a power supply) but in this case the OP wouldn't see 13v at the panel rising to 14v+ when on EHU.
Wonder if it could be a very high resistance connection between battery and PDU? The battery would still 'show' on the PDU but wouldn't actually power anything

.
Suggest the OP unplug the EHU and watches the battery voltage indicator as he turns on 12v equipment.
Oh, those 240v sockets will ONLY work when on EHU BTW.