In the present work we investigate the multiscale dynamics of enstrophy in homogeneous isotropic turbulence by exploiting the two-point formalism provided by the Kármán–Howarth–Monin–Hill approach extended to the enstrophy governing equation. The study is conducted on direct numerical simulations with a Taylor-based Reynolds number in the range of $140\lesssim R{e}_{\lambda }\lesssim 400$. The two-point enstrophy budget at scales $r>10\eta$ appears to be entirely determined by production via vortex stretching, which balances enstrophy destruction, and to be dominated by the diffusive transport at smaller scales, thus preventing the emergence of a range dominated by the inertial transport of enstrophy. Consequently, the second-order structure function of vorticity only shows a viscous scaling $\sim r^2$ at very small scales, followed by a constant behavior at larger scales. This plateau, together with the statistical isotropy, implies that the structure function is equally distributed among its longitudinal and transverse contributions at such scales. The decomposition in longitudinal and transverse contributions also highlights a dual nature of the inertial enstrophy flux. In particular, enstrophy appears to be transferred across scales through a non-trivial combination of direct and reverse interscale transfer. It is shown that the dual nature of this transfer is strictly related to the vortex stretching mechanism, which, in addition to producing enstrophy through vorticity amplification, also transfers longitudinal vorticity towards larger scales (by stretching the vortical elements) and transverse vorticity towards smaller scales (by contracting these vortical elements in the radial direction). The sum of these two contributions results in an overall transfer of enstrophy from large towards small scales. We propose the use of the pressure transport term as a proxy to obtain some information on the dynamics of relevant events of inertial energy and enstrophy transport. The new findings highlight the relevance of inertial compression events in longitudinal energy transport. At the same time, a good correlation between transverse energy transport events and the radial contraction of vortical elements due to vortex stretching mechanisms is also found.