In this study, we employ density functional theory based first-principles calculations to investigate the spin-orbit effects in the electronic structure of a polar-nonpolar sandwich heterostructure namely
LaAlO
3
/
SrTiO
3
/
LaAlO
3
. Our focus on the
Ti-3d
bands reveals an inverted ordering of the
SrTiO
3
-
t
2
g
orbital near the n-type interface, which is consistent with earlier experimental work. In contrast, toward the p-type interface, the orbital ordering aligns with the natural ordering of
SrTiO
3
orbitals, influenced by crystal field splitting. In the presence of SOC, a notable inter-orbital coupling between
t
2
g
and
e
g
orbitals is observed within the tetragonal slab, a phenomenon not reported before in the
SrTiO
3
-based 2D systems. Additionally, our observations highlight that the cubic Rashba splitting in this system surpasses the linear Rashba splitting, contrary to experimental findings. This comprehensive analysis contributes to a refined understanding of the role of orbital mixing in Rashba splitting in the sandwich oxide heterostructures.