Since that 'lower-ab jiggle' is a fat storage area, lowering body fat is more apt to decrease it than are ab or core exercises (though exercises like planks and "witches caldrons"--with forearms on a stability ball in a plank position---can help strengthen the transverse abdominals, which help hold in that area).
You probably do have good abdominal muscles, but they are hidden under a layer (or two) of fat.
Your diet, weight work that includes the larger muscle groups of the legs, back and chest (to burn more calories and stimulate growth hormone) and cardio is what can reduce fat.
As Kadekim indicated, if your body likes to store fat there in particular, you may end up looking 'too skinny' elsewhere if you get to the point where you have flat abs, and may have to learn to love a bit of a pooch.