We demonstrate programmable control of kinetic soliton dynamics in all-Josephson-junction (all-JJ) networks through a novel tunable cell design. This cell enables on-demand switching of transmission lines and operates across defined parameter regimes supporting diverse dynamical modes. By introducing a structural asymmetry into a transmission line, we implement a Josephson diode that enforces unidirectional soliton propagation. The programmability of the kinetic inductance then provides a crucial mechanism to selectively enable or disable this diode functionality. By engineering artificial inhomogeneity into the circuit architecture, we enhance robustness in all-JJ logic circuits, 2D transmission line all-JJ lattices, and neuromorphic computing systems.