In the present work, we investigate the unstationary dynamics of sessile droplets subjected to high-frequency surface acoustic waves modulated at a lower frequency close to the first inertio-capillary resonance mode of the drop. Under the action of both acoustic streaming and radiation pressure, the droplet response combines (i) a directional motion and (ii) oscillations of its shape and contact-line position. The droplet oscillations and time-averaged velocity show strong dependency on the modulation frequency. While the former dependence is linked to some resonance effects (harmonic and parametric), the latter one is still an unsolved issue. To get further insight of the underlying physics, we investigate here the fast oscillating dynamics of the drop contact line and of the dynamical contact angles through high-speed and high-resolution measurements at various modulation frequency. At odds with what is predicted and measured in stationary moving contact lines, we show that the contact-line velocity exhibits complex, non-single-valued dependence with the dynamic contact angles.