Experts and BHG readers answer.
These are two different problems that combine to create a tough situation, one that I think would make it nearly impossible to grow grass there. If you want to try, first you must make sure you have adequate irrigation. Sandy soil = droughty soil. Second, if you can prune any low-hanging branches to improve light levels, do so. Then, raise the mower's cutting height, and overseed with a shade mix (you've probably done this already, but just in case...). If all this still doesn't work, give it up and plant shade-tolerant perennials instead. Columbine, hosta, azaleas, coral bells, bleeding heart, etc. These wouldn't do well in sandy soil, so if you try this solution, be sure you amend the soil heavily with compost when you plant.