Running the wire to the other house shouldn't effect the operation of the alarm. Is the alarm triggered by a float switch like I have in the bilge of my boat? If so, put the alarm unit in your house, and use a two-conductor low-voltage wire to reach the float switch. Your biggest problem will be burying the cable, or running it overhead. UV sunlight overhead, or moisture in the ground will damage the wire, and be the hardest problem to deal with.
Any chance you have a spare pair in a phone cable running between the cottage and the house? Is there a direct burial conduit? An unused coax run?
When I build a garage some distance from my house, I planned ahead, and buried two separate PVC conduits. One for 240VAC for power to the garage. The other for low voltage circuits (which shouldn't be run in the same conduit as 120/240V) which had a CAT5 cable for computer, another for phone, intercom, alarm, and a75Ω TV Coax run.