Hello, my name is Dan.
I will do my best to help you, the only stupid question is the unasked one.
As far as the iPad 2
and 3 there is very little difference.
Both use the same iOS, both use the same email settings, iCloud
No difference there.
What is different with your email is the SMTP settings.
One simple way to check is to goto Settings on both iPads.
Settings/Mail, Contacts, Calendars and select the account that isn't working on both.
Compare the two for settings.
If the new iPad differs then delete that account and recreate it.
Select Add account on the first page in Mail, Contacts, Calendars. Let the iPad do the heavy lifting, you just fill in the blanks when it asks.
Try that and let me know if that does it for you.
If it does not then we will dig deeper.