The current in one 'leg' flows from its hot, through the load and back to the panel in your RV via its neutral. Since it is AC, the flow direction reverses 60 times per second. Meanwhile, the other leg does the same thing but with the flow traveling in the opposite direction to the first leg. From the panel in your RV to the loads, nothing really special happens but between the supply and your panel (i.e. your shore power cord), the neutral only carries the difference in current between the two legs. This is because the neutral is all connected together in your RV panel. Current returning from one leg's neutral just flows out the other leg's neutral without traveling back to the pedestal or power company.
So to your comment about 'canceling out', they do cancel out in that any opposing currents simply don't flow.