The good news is that it's an Ikea couch, so it's just the frame of a couch with a slip cover over it.
The bad news is that they discontinued this one about 5 years ago. So. There's another couch that they have that is similar in size and shape, and I checked on a couple of forums, and people with our couch have been able to use the slip covers for the newer couch with little issue. We haven't decided if we'll buy a new cover or a new couch yet.
I would just like to say that there is nothing that will take permanent marker off of your couch. Any internet troll you might happen upon whilst using your raging google fu that tries to give you some recipe or set of instructions is A LYING TROLL. I tried rubbing alcohol, nail polish remover, Tide pen, dish soap, hairspray...with little to no effect. I ain't mad, though. It could have been worse. She could have doused the couch in lighter fluid and set that junk on fire.