Why not always run from inverter? When on shore power your battery charger is charging batteries...
If you really want to switch, you could use a regular three way switch for homes. The same type used to switch on a light from two locations.
You would tie the black from the wine cooler to the "common" on the switch, the black from shore to any other two and the black from invert to the remaining. Tie all whites together et voila.
'06 Mountain Aire 4309, ISL 400-CM850, Spartan MMGT
'16 Jeep Wrangler