Have you verified that the messages are not getting stuck in the iPad's outbox?
This too. However I would think that the messages would pour out once the machine transitions to the other network.
That's what was puzzling me about this. If the mail simply didn't send, I would think a backlog would go out as soon as the device connected to another network.
DNS shouldn't explain why other addresses work, but it's worth a shot. It shouldn't be too hard to switch her iPad or router to Google's DNS or one of the others in order to test this.