A self join should work for you (and self joins are a good way to maintain a properly normalized structure to your tables). I can't tell from your description why it's not working. You can encounter problems with the data in the key fields (do they really match like you expect), in how the details of the relationship are set up or in how you've structured your layout. I can't tell if any of these issues might be the cause of your problem without knowing more about the tables/relationships and layouts involved.
There is an alternative for your specific case. Are you able to set up a portal that lists all the itinerary records for one traveler? If so, you can specify a sort order for that relationship (or a copy of that relationship) that sorts by your datetime field to make it the first row in your portal. Placing that single related field on your layout without using a portal may well provide what you need.