This paper develops a sequencing-enabled hierarchical connected automated vehicle (CAV) cooperative on-ramp merging control framework. The proposed framework consists of a two-layer design: the upper-level control sequences the vehicles to harmonize the traffic density across mainline and on-ramp segments, simultaneously enhancing lower-level control efficiency through a mixed-integer linear programming formulation. Subsequently, the lower-level control, in turn, employs a longitudinal distributed model predictive control (MPC) supplemented by a virtual car-following (CF) concept to ensure three key aspects: asymptotic local stability, <inline-formula><tex-math notation="LaTeX">$l_{2}$</tex-math></inline-formula> norm string stability, and safety. Proofs of asymptotic local stability and <inline-formula><tex-math notation="LaTeX">$l_{2}$</tex-math></inline-formula> norm string stability are mathematically derived. Compared to other prevalent asymptotic local-stable MPC controllers, the proposed distributed MPC controller greatly expands the initial feasible set. Additionally, an auxiliary lateral control is developed to maintain lane-keeping and merging smoothness while accommodating ramp geometric curvature. To validate the proposed framework, multiple numerical experiments are conducted. Results indicate a notable outperformance of our upper-level controller against a distance-based sequencing method. Furthermore, the lower-level control effectively ensures smooth acceleration, safe merging with adequate spacing, adherence to proven longitudinal local and string stability, and rapid regulation of lateral deviations.