How long is her USC graduate program? I would not want to have to argue that a PhD student at USC who lives off campus in Los Angeles and TAs at USC is not a California resident. Someone in a 9-month MA program is a different kettle of fish.
If you decide that she's going to have to register her car in California, it may be easier to sell the old car here and buy a used car there. It may be really expensive to bring an OOS car into compliance with emissions standards in California.
Check with your insurance broker, too. You are not going to be happy if there's an accident and your insurer denies coverage because the car has been moved to California.