In this work, we investigate theoretically and demonstrate experimentally the existence of valley Hall edge states in the in-plane dynamics of honeycomb lattices with bivalued strut thickness. We exploit these states to achieve nontrivial waveguiding of optical modes that is immune to backscattering from sharp corners. We also present how different types of interfaces can be combined into multibranch junctions to form complex waveguide paths and realize a variety of structural logic designs with unconventional wave-transport capabilities. We illustrate this potential with two applications. The first is a direction-selective energy-splitting waveguide tree featuring a pronounced asymmetric wave-transport behavior. The second is an internal waveguide loop along which the energy can be temporarily trapped and periodically released, effectively working as a signal delayer. The modal complexity of in-plane elasticity has important consequences for the regime of manifestation of the edge states, as the availability of viable total band gaps is shifted to higher frequencies compared to the out-of-plane counterpart problem. It also poses additional experimental challenges, associated with proper acquisition and deciphering of the in-plane modes, the solution of which requires a systematic use of in-plane laser vibrometry.