Dear Ms. Chiavetta,
Thank you for posting your request on History Hub!
The Alsatia sailed the Mediterranean to/from New York service only and therefore, would not have taken your family members to New Orleans. We suggest that you review the Passenger Lists of Vessels Arriving at New Orleans, 1820 - 1902 browsing page by page through the records from 1897 as necessary. The records are arranged by name of ship. For access to the passenger lists, please contact the National Archives at Fort Worth via email at email@example.com. For more background and research tips, please see the National Archives Immigration Records web page.
Please note that, historically, there were any number of ways an individual or groups of family members could have traveled from Ellis Island to their final destination. It is most likely that Loreta and her sons listed their final destination as New Orleans for the initial booking, but may have made prior arrangements for overland transportation with a third party service. Records or documentation for privately arranged overland transportation is not available or may no longer exist.
We hope this is helpful. Best of luck with your family research!
[Information provided by Elizabeth Burnes, Subject Matter Expert