We present a detailed study of the faint Milky Way satellite Draco II (Dra II) from deep CFHT/MegaCam broad-band g and i photometry and narrow-band metallicity-sensitive CaliK observations, along with follow-up Keck II/DEIMOS multi-object spectroscopy. Forward modelling of the deep photometry allows us to refine the structural and photometric properties of Dra II: the distribution of stars in colour-magnitude space implies Dra II is old (13.5 +/- 0.5 Gyr), very metal-poor, very faint (L-v = 180(-72)(+124) L-circle dot), and at a distance d = 21.5 +/- 0.4 kpc. The narrow-band, metallicity-sensitive Cal-IK Pristine photometry confirms this very low metallicity ([Fe/H] = -2.7 +/- 0.1 dex). Even though our study benefits from a doubling of the spectroscopic sample size compared to previous investigations, the velocity dispersion of the system is still only marginally resolved (sigma(vr) < 5.9 km s(-1) at the 95 per cent confidence level) and confirms that Dra II is a dynamically cold stellar system with a large recessional velocity (< v(r)> = -342.5(-1.2)(+1.1)km s(-)1). We further show that the spectroscopically confirmed members of Dra II have a mean proper motion of (mu(alpha)*, mu(delta)) = (1.26 +/- 0.27, 0.94 +/- 0.28) mas/yr in the Gaia DR2 data, which translates to an orbit with a pericentre and an apocentre of 21.3(-1.0)(+0.7) and 153.8(-34.7)(+56.7) kpc, respectively. Taken altogether, these properties favour the scenario of Dra II being a potentially disrupting dwarf galaxy. The low-significance extra-tidal features we map around the satellite tentatively support this scenario.