If you mean that when you connect it to iTunes for the first time it asks if you want to "Set Up as New" or "Restore from Backup", it wants you to select the "Set Up as New". This only means that you are identifying a new device to your iTunes account on that computer. It won't erase the device.
I would recommend that you do these things first before hooking up your wife's device and selecting the Set Up as New option:
1. Open iTunes and sign your Apple ID out of iTunes and sign your wife's Apple ID into iTunes and authorize it:
Account>Sign Out
Account>Sign In
Account>Authorizations>Authorize this Computer
2. In iTunes>Preferences>Devices, make sure that the box at the bottom that says "Prevent iPods, iPhones, and iPads from syncing automatically is checked
Then you can attach your wife's iPad to iTunes, and when you select "Set Up as New", follow the prompts to set up the device in iTunes. Once that is done, click on File>Devices>Transfer Purchases to transfer your wife's iTunes purchases to your library. Your wife can then sync in the normal manner by selecting all of the music that she wants sync'd to her device. The initial sync will overwrite any existing music on the device:
Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB - Apple Support
Best,
GB
Note: After seeing Eric's post, wanted to clarify that I agree with Eric that using Family Sharing is the best way to go if you have separate iTunes Libraries on different computers. If you only have the one library, you can do it either way, but Family Sharing might be easier if you have a good Wifi connection.
GB