This is really a more appropriate question for Chromebook Central than this discussion group, but I'm not certain from your post if your wife currently logs in to her Chromebook with her personal gmail account or with the apps account. If it's her account, she'll need to set up another user account on the Chromebook to use the offline for the apps account. Drive only allows one offline account per profile.
Also, unless she's really going to the middle of nowhere, she shouldn't have much trouble finding WiFi while traveling.