My emails can be viewed by my wife on her phone.
Probably that the second iPhone is configured to check the mail on your account too. If someone knows your Email account, and your password for the account, the person can register your Email account as his/her own and retrieve mail from it.
Try changing your account password and see what happens. And please create a password on a pattern that is not known to anybody, and keep it secure. Is your iPhone paired to her iPhone through BlueTooth?
Check the details of your accounts (Google, etc.) to see if her phone is linked to your account.
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