Free SMTP Server

Option A:
Have a server at home with some free software (hMailServer), it will accept the emails you send on the way, then pass it through to either the recipient directly (like a real SMTP server would, but with a few possible caveats), or pass it through the SMTP server of the ISP

Option B:
configure it with Gmail (you use the SMTP server of Gmail, WITH authentication, so you need a valid Gmail account). You risk having the email read as  "xx@gmail.com on behalf of zz@yy.com" on the other side

Option A through ISP's SMTP is the only sure way it will work.
The caveats are if using your own server to send SMTP mail or Gmail, spam failsafe protection like SPF and other types might block these types of emails, while sending the mail through the ISP server is always trusted.

A professional ISP will allow their SMTP servers to be used world wide though, with authentication enabled so it's not open for abuse.
Having an ISP assigned email address isn't that smart to begin with anyway (changing ISP means changing email address). Either a Gmail address or a your own domain email address have more longevity and are easier to send mail from reliable from whereever you are (if you choose a good web/domain hoster, for instance an Exchange Online subscription for domain xxx.com)
Also, if it's somewhat work/business related, does xxx@verizon.net sound more professional than xxx@yourownbrandorcompanyname.com?

Has she contacted the ISP to see if their SMTP allows authentication to ensure relaying is possible when not on the ISP network.

That question was answered in the original post already.

E-MailRelay is a free open-source project that does nothing but relay email messages.  If setup correctly this should accomplish the objective, providing that it was installed on a computer at home that was always on and always connected to the Internet.
http://emailrelay.sourceforge.net/

Having software/PC running all the time at home isn't an option.

I have already tried the Gmail option but it doesnt seem to work. I have also read the Gmail is no longer allowing people to use them to relay outgoing emails from non google accounts.

Are you positively sure that this ISP does not allow connection to their SMTP from IP Addresses outside their own range, even if the connection is secure and authenticated?  As has already been pointed out, most ISPs allow this as long as the connection is authenticated.  Check the SMTP settings on the iPad.  Is it setup with a username and password for outgoing messages?

Most ISP's offer webmail.  Perhaps webmail could be used for sending out messages when away.

That's always an option, but will be a pain for the iPad user since:
Always have to start webmail seperately in a browser (if password remember option isn't working, also needs to input username/password every time).
After sending email, it won't appear in the correct Sent Items folder (for instance, if POP3 is used on the iPad).

I allowed the customer to use my free turbo-smtp account as she only sends a couple of emails per day.