how to stop my wife's email from appearing on my ipad?

Are you sharing an AppleID?

If all your devices are sharing a common AppleID for iCloud, you’ll encounter all kinds of issues with unintentional and/or unwanted sharing of sensitive/private information. You’ll not be able to reliably maintain any kind of data separation.

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). 

With the sole exception of Apple Mail (this being associated with your AppleID), whether or not you share a single AppleID or not, Mail accounts can be installed on multiple devices. If you don’t intend to share an email account, you should only install your own email accounts on your own device.

Removing unwanted Mail account is easy - as is adding an account that you do wish to see on your own devices:

Add and remove email accounts on iPad - Apple Support

If you share appleID then you can’t and you should never share appleID if you do you are the same person in all things apple if you do not then read

Add and remove email accounts on iPad – Apple Support (UK)