Since your house outlet appears to be safe from your testing
Question on your main panel:
Is it a 200 amp equipped with a separate ground bar attached to two ground rods sunk outside the house ?
also are you running your sub panel off a 50amp or more breaker with at least a 12 - 2 burial wire
Trying not to confuse you, just being safe
on your wiring to the sub panel I take it you ran the:
blk wire to the breaker the white to the neutral bar and the copper bare wire to the ground bar?
Your Election is right about sinking a separate ground rod for your sub box
for you might be getting a little feed back on the neutral side