I planned for this exact event (just in case), however my tank is inside of a wall, so my "tray" is hidden in the bottom cabinets. It may be harder for you if you have a free standing aquarium in the living room. But anyway, here's what I did....I cut a drain hole in the floor and put a metal drain cover over it. Next I put in a rubber membrane (like the one's they use for showers before the tile is put down). I covered this with a light concrete coating, sloping everything toward the drain. The drain leads out of the house and into the gutter system. So, if there ever was a major burst or overflow, hopefully most of it would go down the drain. This drain is also helpful when doing water changes. I just let it run down the drain.
This is more of "permanent" thing though. I wouldn't go drilling holes in the floor of your Dad's house without approval. On the other hand, it would take a mighty big "tray" to catch ALL of the water if you had a break. If you are just worried about overflow water, then just keep your sump at a level no more than what could ever reach the top of the rim in case of anything going wrong.