  Spin-orbit dynamics and relativistic corrections to the kinetic energy in
strong-field dynamics, have long been ignored for near- and mid-IR fields with
intensities $10^{13}$--$10^{14}$ W/cm$^2$, as the final photoelectron energies
are considered too low for these effects to play a role. However, using a
precise and flexible path-integral formalism, we include all correction terms
from the fine-structure, Breit-Pauli Hamiltonian. This enables a treatment of
spin, through coherent spin-states, which is the first model to use this
approach in strong-field physics. We are able to show that the most
energetically rescattered wavepackets, undergo huge momentum transfer and
briefly reach relativistic velocities, which warrants relativistic kinetic
energy corrections. We probe these effects and show that they yield notable
differences for a $1600$ nm wavelength laser field on the dynamics and the
photoelectron spectra. Furthermore, we find that the dynamical spin-orbit
coupling is strongly overestimated if relativistic corrections to kinetic
energy are not considered. Finally, we derive a new condition that demonstrates
that relativistic effects begin to play a role at intensities orders of
magnitude lower than expected. Our findings may have important implication for
imaging processes such as laser-induced electron diffraction, which includes
high-energy photoelectron recollisions.
