For core I'd do reg crunches, side crunches, cross leg crunches, seated twists w/ medicine ball, supermans, reverse crunches...lots of that stuff because, along with your hips, your core provides the most velocity. I'd throw in some forearm workouts too like wrist curls, wrist extensions, hammer weights, squeezers (those things your squeeze with your hands). If dumbell rows and posterier raises weren't on there Id do that too. Stephen Ellis' dumbell exercises are good, I'd use his thereband excersises along with those.
And instead of dividing everything into just a few lifts a day, I'd do all the lower body one day, upper body the next, and alternate like that so you get more of a workout.