can't use motor mover whist mains plug is connected , because the motor mover main switch is in way now ?
I think that is done by design to prevent you from using the mover when EHU is plugged in.
Either of your suggested options would work.
Option A, another mains socket. The issue here may be physically running the cable. I wouldn't want it under the caravan without some form of mechanical protection - it could easily be damaged by being hit by a stone or grounding out. If the cable could be run inside the caravan it's the option I'd go for.
Option B. It would probably be easier to fit a second motor mover switch and wire them in parallel. (It would remove the need to reseal the battery compartment after removing the switch).
In both cases you would need to be careful not to use the motormover with the EHU connected. The obvious issue doing this would be stretching the EHU cable, but I suspect that it could also overload your 12v power supply
Edit. Thinking about option A in relation to Mr Plods post, the 240v bit fixed to the caravan is the plug (the pins are exposed). Fitting a second on the other side of the caravan without some means of switching between them would mean that 240v conductors (the live and neutral pins) would be exposed on the one that didn't have the EHU connected to it. Not an ideal situation and almost certainly breaches regulations somewhere.