Joy, my syncro came in your (new) state.  I just
make sure I plug the shore power cord in in the
correct orientation.  (Ground down)  Then, all
will be well if you use the fridge or plug two-
prong gizmos into the interior receptacle.

If the shore power cord is plugged into a ground-
fault outlet, which it would in all modern wiring
sitautions, then you are very safe, since the
ground-fault compares the positive and neutral
and doesn't look at the ground, and is much more
sensitive than a circuit breaker.  Then even a
three prong gizmo would be safe unless it was a
surge protector trying to dump a spike to the ground.

The code today allows three prong receptacles to be
installed in a house with two-wire wiring if they are
"behind" a ground-fault receptacle.  Again, the
situation that is not protected is a protector that
wants to dump to ground rather than shut off.

                        Richard A Jones
                        Boulder, Colorado