Your first paragraph is correct. I have no clear idea why your instructor said you had to put your pistol in the trunk in NN and Yorktown. The Yorktown Battlefield Park is Federal Territory as is the Colonial Parkway, so there, the firearm must be stored away. Otherwise you can carry openly to your heart's content in Yorktown. It's a bit more likely you'll be hassled in NN because the political climate is more urban there. Just the same, I have open carried extensively in both places for about 2 years with no problems at all.
Disturbing the peace? I think that would be a false arrest, since open carry is NOT ILLEGAL in VA, and you can't be charged with a crime for doing something that isn't a crime, right?
Check out the numerous threads in this site, and you'll see many references to OC in NN and York.