You're welcome! But please re-read my point #1. You'll see that confirmation numbers (also known as record locators and PNRs) are different from ticket numbers. United should be able to give you your Thai and China confirmation numbers, though there is a small chance it will direct you to those other airlines for that information...and as I'd said you'll likely need to call them anyway for seat assignments.

To make a long story short, ticket numbers are more important than confirmation numbers, but confirmation numbers are used for most purposes in communicating with the airlines (such as seat assignments). Again, make sure that for each flight each of you has a ticket number (which could well be the same for all of the flights) and a confirmation number (which will likely differ, depending on the airline).