In reply to thomasmouse:
i think 'core' is a marketing ploy. in most cases its sold as what youve described - low level hip flexor and abdominal exercises, maybe some peripheral muscle group sttuff thrown in to sell bouncy balls.
at a more developed level the idea relates more to integrating the larger muscle masses of the torso and around the pelvis and shoulders with the musculature extending out into the arms and legs - a fairly massive and complex chunk of the body thats mosty hidden behind the only bits that many people ever train (and most of which is unsurprisingly very frontal).
stick with what youre doing but increase the range of motion and orientation to activate the sides and back, and up the complexity of the movements to include the limbs.
a lot of alll this is best trained in bits, then put together.
good examples are dumbell presses in the suspended position off a ghd, turkish get ups, rope pulls, lunge presses - all stuff that demands the torso connects the limbs when weighted/under stress.
bouncy balls? dunno. some sort of warm up maybe.