解:
(1) 因为$\dfrac{1}{2} \ge 0,$所以$\left⟨ \dfrac{1}{2} \right\rangle = 2×\dfrac{1}{2} - 3 = 1 - 3 = -2。$
因为$-2 < 0,$所以$\left⟨ -2 \right\rangle = -2×(-2) + 3 = 4 + 3 = 7。$
(2) 当$a=3$时,$a\ge0,$则$\left⟨ a \right\rangle = 2×3 - 3 = 3。$
当$b=-4$时,$b<0,$则$\left⟨ b \right\rangle = -2×(-4) + 3 = 11。$
所以$\left⟨ a \right\rangle - \left⟨ b \right\rangle = 3 - 11 = -8。$