We present a kinematic study of a thousand of dwarf satellites of MW/M31-like hosts from the IllustrisTNG50 simulation. Internal kinematics were derived for all the snapshots to obtain a historical record of their rotation velocity in the plane of the sky (|VT|) and the amplitude of their velocity gradients along the line of sight ($A_{\rm grad}^{v_z}$) measured from the host. For the majority of the satellites, we initially detected rotation in the plane of the sky (65 per cent) or velocity gradients (80 per cent), and this was progressively reduced to 45 per cent and 68 per cent at z = 0, respectively. We find that the evolution of the rotation in the plane of the sky and the velocity gradients differs according to type of dwarfs, which could be explained in terms of their different masses and orbital histories. We observe that interaction with the host has an impact on the evolution of the internal kinematics of the satellites. The rotation signal of the satellites is progressively reduced during pericentric passages, the first pericentre being especially disruptive for the initial kinematics. We observe temporary increases in $A_{\rm grad}^{v_z}$ during pericentric passage caused by tidal interaction with the host, $A_{\rm grad}^{v_z}$ increasing as the satellites approach their pericentre and dropping as they move away. In summary, we conclude that the presence of detectable rotation in dwarf satellites is not uncommon, and that the evolution of their internal kinematics is clearly affected by their interaction with the host.