  We present an analysis of the kinematics of fourteen satellites of the Milky
Way (MW). We use proper motions (PMs) from the $Gaia$ Early Data Release 3
(EDR3) and line-of-sight velocities ($v_{\mathrm{los}}$) available in the
literature to derive the systemic 3D motion of these systems. For six of them,
namely the Carina, Draco, Fornax, Sculptor, Sextans, and Ursa Minor dwarf
spheroidal galaxies (dSph), we study the internal kinematics projecting the
stellar PMs into radial, $V_R$ (expansion/contraction), and tangential, $V_T$
(rotation), velocity components with respect to the centre-of-mass. We find
significant rotation in the Carina ($|V_T| = 9.6 \pm 4.5 \ {\rm{km \
s^{-1}}}\>$), Fornax ($|V_T| = 2.8 \pm 1.3 \ {\rm{km \ s^{-1}}}\>$), and
Sculptor ($|V_T| = 3.0 \pm 1.0 \ {\rm{km \ s^{-1}}}\>$) dSphs. Besides the
Sagittarius dSph, these are the first measurements of internal rotation in the
plane of the sky in the MW's classical dSphs. All galaxies except Carina show
$|V_T| / \sigma_v < 1$. We find that slower rotators tend to show, on average,
larger sky-projected ellipticity (as expected for a sample with random viewing
angles), and are located at smaller Galactocentric distances (as expected for
tidal stirring scenarios in which rotation is transformed into random motions
as satellites sink into the parent halo). However, these trends are small and
not statistically significant, indicating that rotation has not played a
dominant role in shaping the 3D structure of these galaxies. Either tidal
stirring had a weak impact on the evolution of these systems, or it perturbed
them with similar efficiency regardless of their current Galactocentric
distance.
