I'm assuming you're using Yubico Authenticator to generate a 6-digit TOTP code (this is the only option I'm aware within Amazon accounts that works with a YubiKey)? If so, have you tried inserting the YubiKey in both computers (one after the other) to see if the codes match? Since it's TOTP, the most logical issue would be that the system times are too out of sync (every time-based implementation is going to have a set amount of time/codes that are considered satisfactory and will be accepted for login). It's important to check the system time first. If the same or within a minute or two, try comparing the timezone settings on both systems to make sure they are correct (I've seen cases where one computer had the correct local time but was set to another timezone, so the actual time was 1 hour off minimum).