A pump-probe scheme for preparing and monitoring electron-nuclear motion in a dissociative coherent electron-nuclear wave packet is explored from numerical solutions of a non-Born-Oppenheimer time-dependent Schrödinger equation. A mid-ir intense few-cycle probe pulse is used to generate molecular high-order-harmonic generation (MHOHG) from a coherent superposition of two or more dissociative coherent electronic-nuclear wave packets, prepared by a femtosecond uv pump pulse. Varying the time delay between the intense ir probe pulse and the uv pump pulse by a few hundreds of attoseconds, the MHOHG signal intensity is shown to vary by orders of magnitude, thus showing the high sensitivity to electron-nuclear dynamics in coherent electron-nuclear wave packets. We relate this high sensitivity of MHOHG spectra to opposing electron velocities (fluxes) in the electron wave packets of the recombining (recolliding) ionized electron and of the bound electron in the initial coherent superposition of two electronic states.