The clients are syncing with the sync store in Dropbox, not with the database(s) itself. Double check the sync settings on your wife’s iPad, there is probably an error. Sometimes it’s best to just reinstall DTTG and start over.
(I sync two iPads and an iPhone to the same sync store without issues – and my scenario is not unusual. So success is possible.)
Are you Syncing to a shared Dropbox account? If you’re Syncing to your Dropbox account, she would have to use your account and credentials on her device too.