I take it it's an ADSL system. In that case NO you can not have two modems/routers coming off the same telephone line (hence you were asked the question in post #2 whether they wanted it in both locations)
The ONLY safe ways are as follows
- Get BT to put in a new phone line (Not an extension) (or get vm cable routed to the barn) and pay for a 2nd broadband
- Get a decent Wifi system (probably a N rated 5ghz bridged system with directional antennas)
- Get 100m of CAT6 and bury it in conduits
A suspended cat6 will work, all the way until the nearest thunderstorm which will probably drop out the entire network (the cat6 and suspending wire will act like a huge ground plane for interference and surges). You could get shielded CAT6 but it's really expensive and means extra weight and might still not protect you from local lightning (it doesn't need to hit the wire to cause a surge, anything within 10 miles can cause enough of an EMP