The XT Mobile broadand sticks will require authenticated mail settings (ideally use Orcon's authenticated mail settings). 

older CDMA T-Sticks allow unauthenticed mail relay (smtp.xtra.co.nz) to send for mail service providers who did not provide authenticated settings, but XT requires authentication 
 
The issue is with incredimail as an email program (limited settings for the free client, no support, no encryption).

Recommended steps - change from Incredimail to something else:

Install thunderbird http://www.mozillamessaging.com/en-US/thunderbird/ 

Call Orcon and explain you need the secure authenticated email settings
No SSL encryption means that your mother's username and password are sent in the clear. See what they can do to enable SSL as this is poor email administration from a large NZ ISP.

The information that Orcon has about their email settings
http://www.orcon.net.nz/support/page/what_are_your_pop3_settings_for_orcon_email/
http://www.orcon.net.nz/support/page/can_i_use_orcon_email_while_overseas/

If possible with Incredimail - export the email addressbook/contacts, and save the file to the desktop.
Import the addressbook/contacts from the desktop to Thunderbird.
This way your mother can easily compose and send using her existing contacts and email account.

I would advise against changing from her Orcon email address to gmail as it requires her friends and family to update their addressbooks - which if it is anything like my mother, who still sends to my old email address I haven't used in 5 years.