Smooth electrostatic gates generally have little ability to mix atomic valleys, whose large momentum separation requires short-range perturbations. In moiré superlattices, the relevant valley extrema can instead be separated by much smaller momenta, opening a route to gate-controlled valley hybridization. Here we investigate this mechanism in gate-defined quantum dots in twisted WSe${}_2$ bilayers. Using a continuum model, we show that smooth lateral confinement produces a lowest-orbital doublet associated with the two moiré valleys. The confinement radius and depth tune the hybridization between these states, while a displacement field controls their detuning. These dependencies are captured by an effective two-level Hamiltonian with two noncommuting electrostatic control terms. For small dots, the valley splitting reaches several hundred microelectronvolts, while the doublet remains separated from excited orbitals by energies on the millielectronvolt scale. These results demonstrate electrical control of moiré-valley hybridization and identify the confined valley doublet as a promising candidate for a valley-based qubit.