Since you already have a Local Server (mounted on the rover I suppose?) why not keep it running all the time on dock power (and charging) when docked and obviously on battery when roving.
PS if you have further details on the build etc, I would love to see themā¦ That is like the type of rover I wish I had the energy to build. It even includes LEGO for the win!! 
One of these days I plan to move an RPi onto this for the brain with some autonomous operationā¦ Gunnerator