We investigate the energy spectrum of a single- and two-electron quantum dot (QD) embedded in two-dimensional electron gas at the interface between
SrTiO3 and
LaAlO3, in the presence of the external magnetic field. For this purpose, the three-band model of
3d electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low-energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one
dxy orbital with the spin-orbit interaction originating from the coupling to the
dxz and
dyz bands. This is not the case for stronger confinement where contribution of the states related to the
dxz/yz orbital is relevant. Based on the time-dependent calculations, we discuss in detail the manipulation of the electron spin in a QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in detail with respect to the parity selection rule. Our calculations show that, for a single-electron QD, the spin flip in the ground state has the character of a Rabi resonance, while for two electrons, the singlet-triplet transition is forbidden by the parity symmetry. For the two-electron QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.