If your wife's email account is a sub-account, it is the master email account's security questions and answers that need to be entered.
If that does not work you will need to contact BT, have your BT account number handy and they should either be able to reset the password for you or send you a pin code to your registered address so that you can use that to change the password.
If you saved the password on the iPad you should check to see if you can view it on the iPad.
See links
http://osxdaily.com/2014/06/26/find-saved-passwords-ios/
The other thing you should be able to do is back up the "Old" iPad and transfer its contents including any passwords to the "new" iPad.
See links
http://osxdaily.com/2012/03/16/transfer-old-ipad-to-new-ipad/
https://support.apple.com/en-gb/HT201269