Abstract Recent advances in quantum dot platforms have opened a new platform for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological √X X - and X -quantum gates in an interacting Y -shaped quantum-dot array. The proposed architecture enables both braiding and charge readout through simple fusion operations controlled by gate-tunable potentials. Using many-body time-dependent exact diagonalization, we analyze MZM braiding and fusion dynamics in the presence of nearest-neighbor Coulomb interactions, hopping-pairing mismatch, onsite charge fluctuations, and pairing disorder. We compute diabatic errors, braiding fidelity, and the time- and space-resolved electron and hole components of the local density of states to monitor the braiding process. Our results show that even weak interactions or pairing disorder induce oscillations in the braiding fidelity, thereby setting an upper bound on the braiding speed. Furthermore, we demonstrate that comparing fusion outcomes before and after double braiding provides a direct and experimentally accessible signature of the non-Abelian nature of MZMs in quantum-dot systems.