If you are using an email client/app it would appear that when you set up the app you have set it to check and fetch email from both the BTMail account and the gmail account.
This will cause BTMail and gmail to be checked and as you have probably set them up as IMAP accounts the emails will show on all the devices that you have set up to access the email accounts.
If this has only started since you set up her phone you need to go into the phone's email apps settings and check to see if both the email accounts are showing there, probably under the "General Settings" where it should show the accounts that the app is checking. If you don't want them both checked by that email app you should delete one of the email accounts from the app.
Then download and install another email app and set that up to access the email account that you have deleted.
Without having access to your devices obviously the above is just guess work on my part.
