I don’t really distinguish between national heritage and national identity. Thinking about it now, I guess national heritage can be more detailed about facts and specific objects, where as national identity is more of an attitude.
I don’t consider the history of Native Americans to be a part of U.S. heritage to the same extent that I consider European history to be a part of it. In my opinion Native American heritage is U.S. heritage to the extent that we live on the land that they used to live and, when applicable, to the extent their people have assimilated and bring their heritage and culture with them. For the most part I identify with the early Europeans who settled in the Americas more than the indigenous peoples already here, who they were in conflict with.
ETA: Example, I don’t consider myself a Seminole, I don’t identify with them, and I think it would be highly offensive to do so. But there are some place-names and local traditions that ultimately go back to when the Seminole tribe occupied this land. And the Seminoles have undoubtedly shaped local history.
Well, I’m sure the two hemispheres would come into contact eventually. I can’t say whether our history would be remotely similar if Columbus had not made his voyages.
ETA2: Also, I live/grew up in Florida. So, you know, Ponce de Leon, St. Augustine… predates and is more relevant locally than Jamestown.
~Max