As I recall, Alexis first tried dialing his number, which didn't go through, and then switched to using Skype, which I gather is some sort of online videophone service. Maybe with Skype you don't need an international code.
(Ohh, look at us... two professional science-fiction authors struggling to keep up with present-day technology.
Not using Skype but having installed it for my dad i can say that with Skype it's basically a chatprogram you can use with text, voice or video. You log in and then you can contact anyone you have in your list of Skype contacts (provided they have the program running at the same time of course). This works because it's an internet based program and uses Voice over IP protocols (my dad uses it sometimes to call me in Germany because it's much cheaper than using regular telephone).
It's also making sense to try it that way for Alexis because she can assume that her dad is keeping all modes of communication open in case she can contact him (and because of the internet connection/cell tower location it's also dead easy for law enforcement to track her position).