HI jrpierson,
Thank you for posting your query in Microsoft community!
I will guide you regarding this issue.
1) You want to resync the second PCs morden UI?
Method1:
I would like to suggest you to refer the link.
Should I sync settings between PCs?
http://windows.microsoft.com/en-IN/windows-8/sync-settings-pcs
Method2:
I would like to suggest you to follow the steps to restore missing apps.
Step 1:
Switch to start screen. Type Desktop and press enter key to see desktop in search result. Novice users may like who would like to type in the Search box can use Windows + Q hotkey to see the Search charm.
Step 2:
Right-click on desktop result to see the app command bar (the bar that appears at the bottom of the screen) and then click pin to start option to pin Desktop tile to the Start screen. You are done!
Method3:
I would like to suggest you to run the account troubleshooter and check.
http://download.microsoft.com/download/F/2/4/F24D0C03-4181-4E5B-A23B-5C3A6B5974E3/microsoftaccounts.diagcab
Please post back with the required information. I will be glad to provide you with the additional options available that you can utilize to get the issue resolved.