Is it possible to connect 3 sealed lead acid batteries in both parallel and series at the same time like in the diagram below?
To achieve this you would to wire all the connections back to a couple of relays and just switch between them as needed. You'd need to be careful to prevent energising both relays simultaneously, achieving a dead short as pointed out in a previous answer. To do this you could wire the signal to Coil 1 through a NC (Normally Closed) contact on the opposing relay. When you energise Coil 2, the NC contact will open, preventing current travelling to Coil 1.