Your wife should have her own gmail account that is only set up on her devices or user account. Or, remove the current account from TB. It's probably set up as IMAP on the the computer and phone, so the mail is synced between devices. Also, gmail automatically copies messages to the Sent Mail folder. If the account were set up as POP on the phone, all sent messages would be stored only on the phone - but the mail wouldn't be synced with other devices.

Thanks but I need to see emails she receives but not ones she sends. (Don't ask, it's complicated!)

Messages sent from TB on gmail are automatically copied to Sent Mail. Other apps might copy to Sent Mail or Sent. If you unsubscribe both folders, sent messages won't appear in TB. Still, if someone replies to a 'confidential' message sent by your wife, quoting the original message, then you will see it in the replied message.

All of these workarounds are clumsy; she should have a separate account, if only for confidential mail.

Thanks, it looks like that's the only answer. We used to use Windows Live Mail until it was killed off and that never gave this problem.....progress!!