Quantum sensitivity is an important issue in the field of quantum metrology where sub-Planck scale structures play crucial role in the Heisenberg limited measurement. We investigate the mesoscopic superposition structures, particularly for well-known cat-like and compass-like states, in the rotating Morse system where sub-Planck scale structures originate in the dynamics of a suitably constructed SU(2) coherent state. A detail study of the sensitivity analysis reveals that rotational coupling in the vibrational wave packet can be used as a probe to enhance the sensitivity limit in a diatomic molecule. The maximum sensitivity limit is identified with the rotational amendment, and a quantitative measure of the angle of rotation for different rotational levels is also given. The correspondence of the numerical result with the angle of rotation is also delineated in phase-space Wigner representation.
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