In terms of wifi setup, I would think the easiest way would be configure a wireless router to use a private network at home (10.x.x.x or 192.168.x.x), provide DHCP support, and locked to the 2-3 devices you are going to use (PC, Arduino, phone) and then bring that router to the remote area, complete with PC (initially, later just phone). The router handles all of the wifi infrastructure support, DHCP serving, etc. but you don't actually plug in a connection to the internet, but plug in the PC (unless it has wireless support). It is easy to test at home before trying it out in the field. In the USA you can get these routers for $15 or so.
I would suspect that the Arduino wireless support only has enough support for it to make connections. It probably doesn't have the more general support that is inside of the router. As I said if you look around you can get wifi repeaters as well.