I had the same problem. I renovated last summer and bought a new area rug for the family room. Muffs started using it as a scratching mat, even though she's never bothered with my other rugs. Darned if I know what she liked so much about this new rug. Perhaps there's something about the smell of new rugs.
In any event, a little later, I bought the Ultimate Scratcher (a very tall scratching post), and I decided to put it on the rug right when one first walks into the room (obviously not in a place where I would trip over it!). Since doing so, Muffs now uses the Ultimate Scratcher and rarely scratches the rug anymore (she still does now and then, but maybe once a week, so I can live with that).
I can't say whether this approach will work as well for you as it did for me, but you might try re-locating one of their scratching posts to the living room, or getting another one for the living room (doesn't necessarily need to be the Ultimate Scratcher). Alternatively, if there's one particular spot on the rug where they scratch a lot, try putting a scratching mat there.