I'm assuming you're using the Google Play Music app on both devices and that you uploaded some music to Google's cloud music service using your gmail account.
1. Start the Play Music app on your wife's tablet.
2. Tap the menu bar at the upper right of the app and choose "Settings".
3. Tap "Google Account" and then tap the "Add Account" button.
4. Tap the "Existing" button and fill in your email and password, then tap the right-arrow icon.
I only have one gmail account so couldn't really test beyond this point, but I expect the rest of the process should be pretty straightforward.
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