My guess would be left lumbar nerve root impingement; turning left can close down the left facet causing pain; prolonged sitting can increase the disc herniation leading to n. root compression; does she get any relief leaning forward and to the right? Lets assume for treatment's sake that the disc is slightly effacing the nerve root on image and that the nerve root is inflamed; too much lumbar extension will compress the nerve root and too much flexion (or sitting) will herniate the disc further into the nerve - so what to do? First get on anti-infl meds, a little ice to left low back and avoid aggravating symptoms, maybe? You are right on with the core strengthening in my opinion, just be careful not to aggravate sxs in the process; if she has trouble sleeping due to pain, then it is important to find a position of comfort; this may improve morning sxs; this type of condition can be very slow to improve in some cases; good luck