Dear myked, you will need the charger for the solar panel-battery side, whenever there is sunlight, the charger will do its job, IMHO you won't need a 2A charger there. Battery-load side can be under control of the arduino, it can check the battery voltage through its analog inputs, and when its below the threshold value it stops. You can start doing this by a literature search, similar projects, schematics, and then constructing your own schematic.