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Topological phases of matter, sound, light, and vibrations have enabled brand new routes to direct and control signals at high fidelity. Chern insulators are known for outcompeting other reciprocal systems in terms of their robustness against crystal imperfections and defects. For sound waves we present the combination of a Chern insulator and a valley-Hall-based configuration and explore novel valley-Chern phases that enable both nonreciprocal band inversion processes and bandwidth broadening of valley-polarized one-way interface states. Interestingly, we find that a valley-Chern system made of two adjacent insulators of which one only breaks the time-reversal symmetry, enables entirely robust waveguiding appearing quantitatively equivalent to the classical Chern insulator. Beyond the rich physics presented, we foresee that our findings may stimulate new research in terms of acoustic waveguiding and control.