First there is no default for email like there is for SMS. You're email will go to which ever app you set up. Note: If you set up two email apps with the same email you would get two notifications and so on... So to make Gmail your "default" app, enter all of your email account information in to the Gmail app. I mean for all of your accounts that you want handled in this app. Next delete all account information from the offending app. We don't know what app that is so we can't explain how to do that. It could be as simple as deleting the app cache and data for the offending app or you may have to go into the app and actually delete each account. Finally leave the offending app blank or disable it. Not all preinstalled apps can be disabled, especially on Samsung.
Now all of your email should be directed to and moving through the Gmail app.
This may not solve your notification issue so let's make sure Notifications are on and set up. This flow should work on most Android models. Settings>Applications>Gmail>Notifications, select each account you want to receive notifications for by selecting Show notifications and then personalize the notifications for that account by selecting Mail. Just a note, touch the word Mail and not the slider to customize. Under Mail you can set the ringtone, vibration, app icon and privacy level.