We study the influence of dual-cavity optical feedback on the emission dynamics and timing stability of a passively mode-locked semiconductor laser using a delay differential equation model and verify the timing stability results by an initial experiment. By bifurcation analysis in dependence of the feedback delay times and feedback strength bistability, quasiperiodic and chaotic dynamics, as well as fundamental mode-locking are investigated, yielding a comprehensive overview on the nonlinear emission dynamics arising due to dual-cavity optical feedback. Optimum self-locking ranges for improving the timing stability by dual-cavity optical feedback are identified. A timing jitter reduction and an increase of the repetition rate tuning range of up to a factor of three, compared with single-cavity feedback, are predicted for the parameter ranges investigated. Improved timing stability on short and long timescales is predicted for dual-cavity feedback through the suppression of noise-induced fluctuations. Based on the numerical predictions, experimentally, a maximum timing jitter reduction up to a factor of 180 is found, accompanied by a side-band reduction by a factor of 58 dB, when both feedback cavities are resonant.