If you can string a doorbell wire between the two locations, you can also string an Ethernet cable. Add an Ethernet switch (not router) and/or a WiFi Access Point to the new location, then you can add whatever networked devices you deem useful. Perhaps a baby monitor type 'videophone' that works over Ethernet or WiFi...

Doorbells generally operate using about 16 volts AC up to maybe 24 volts, in my experience. 12 volts AC can work in a pinch, but not all ringers will respond to a mere 12 volts. So there is a transformer involved to reduce the mains voltage down to doorbell safe voltages.

Wiring for doorbell use is entirely non-critical. Almost anything that conducts will work. Two wires from the button to the ringer, another two from ringer to transformer.

Basic wired intercom wiring is similarly non-critical for short distances. Some can work with only two wires, others need four or six wires. If you have a local electrical/electronics scrounger/recycling guy he may know where to source this sort of thing.

Outside the box? Perhaps a hands free (speakerphone) type telephone with a one button auto dial to your phone number.

Running telephone, cable TV and other such wiring around the outside of buildings is a time honored solution. I recently wrapped Ethernet cabling around two sides of a two story house to solve a 'you can't get there from here' WiFi problem. If you are worried about weather exposure you can run the wires inside plastic plumbing piping. Minimize or eliminate the pipe glue will make it easier to thread wires and make changes later.