I, too, have found some rugs to be particularly tricky to grab. The best I can offer you is to entirely remove the bed and nightstands, then click around until you are able to select the rug.
You could also try removing the bed, nightstands, desk, and other furniture then completely delete the floor. You can replace the floor by grabbing that "patio" foundation in the wall sections and dragging it until it refills the room. Then you'll need to re-paint the floors and re-place all the furniture you moved out of the way.
Some apartments come with built-in features that cannot be removed (like fireplaces), but I don't remember a yellow rug that looks to be from a stuff-pack to be on that list. You should be able to select it.
Also, resizing objects makes them more difficult to grab. If the rug is resized, you'll have to grab more near it's dead-center to actually select it.
Good luck!