It would be cheaper in the long run to get a good N router and WiFi card for your grandmother's system - such as this router
and this card
. I have the same router, and can pick up the AP from my parents home - 300 feet away. It's fairly weak, but that's the range possible. YMMV, however...
Depending on the town/municipality codes, you might not be able to hard-wire this connection yourself. You more than likely will need a permit, and a certified electrician to approve it.
For best protection against the elements, ideally, the conduit would enter your home through the foundation or wall, then travel underground - below the frost line if possible to keep the conduit from heaving - to the trailer. Then the conduit could be brought into the trailer's wall - again to keep out the elements.