Syncing

Are you using the same Apple ID?

If so, create a new one for one of the devices, apps and other content can be shared via Family Sharing after that.

Family Sharing - Apple

If you don't want to use a new Apple ID, and you are using iCloud Photos, make sure that sharing iCloud photos, Photostream or shared albums is not enabled on your wife's iPad in the settings for iCloud.

This can only occur if your are sharing an AppleID account. Every user should have their own unique AppleID account - which should be used with all of their own Apple devices.

The Golden Rule: Don’t share an AppleID between users. Each user should have their own AppleID for their own exclusive use - linked to their own primary email (and secondary/recovery email addresses and trusted telephone numbers). 

You should each have your own AppleID - as using a shared AppleID has implications for privacy and unintentional data sharing. There are many good reasons to keep your digital identities entirely separate:

How to create a new Apple ID – Apple Support

Should you wish to do so, you can continue to share Apps, Services, Purchases and Subscriptions using the Family Sharing features.

Family Sharing - Apple

What is Family Sharing? – Apple Support

Set up Family Sharing – Apple Support

Share App Store, iTunes Store and Apple Books purchases with Family Sharing – Apple Support

https://www.imore.com/how-set-up-family-sharing-iphone-ipad

Sharing an AppleID between users is a very bad idea. Sooner or later, you’re going to encounter data loss, account lockout or compromise of sensitive data.