  We present new spectroscopic observations of the diffuse Milky Way satellite
galaxies Antlia 2 and Crater 2, taken as part of the Southern Stellar Stream
Spectroscopic Survey (S5). The new observations approximately double the number
of confirmed member stars in each galaxy and more than double the spatial
extent of spectroscopic observations in Antlia 2. A full kinematic analysis,
including Gaia EDR3 proper motions, detects a clear velocity gradient in Antlia
2 and a tentative velocity gradient in Crater 2. The velocity gradient
magnitudes and directions are consistent with particle stream simulations of
tidal disruption. Furthermore, the orbit and kinematics of Antlia 2 require a
model that includes the reflex motion of the Milky Way induced by the Large
Magellanic Cloud. We also find that Antlia 2's metallicity was previously
overestimated, so it lies on the empirical luminosity-metallicity relation and
is likely only now experiencing substantial stellar mass loss. Current
dynamical models of Antlia 2 require it to have lost over 90% of its stars to
tides, in tension with the low stellar mass loss implied by the updated
metallicity. Overall, the new kinematic measurements support a tidal disruption
scenario for the origin of these large and extended dwarf spheroidal galaxies.
