Okay, here's an idea. Get the app Boxcar from the App Store (it's free or you can pay (in app) $4.99 (USD) to get rid of the ads...).
Boxcar is a notification system that you can personalize. You can set it up to push you all your e-mail notifications from any/all accounts on the iPad.
So, if you follow Boxcar's directions to load each e-mail address separately, there is a point in the process where you can select different sounds for each different e-mail address.
Then, you can set "Fetch New Data" for the Mail app (in Settings under Mail, Contacts, Calendars) so that Push is off and then fetch is manual.
Yeah, you'll still have to use the same Mail app - but at least the sounds can be different so y'all know who got mail.
Again, Boxcar, with ads, is free. May be worth a shot to try? Note that I've not tried this, it justs seems as if it can be done, given what I know about Boxcar (which I have and use daily).
Good luck and let me know if this works (or if you have questions).
Marilyn