The effects of reduced dimensions and the interfaces on antiferromagnetic quantum criticality are studied in epitaxial Kondo superlattices, with alternating n layers of heavy-fermion antiferromagnet CeRhIn_{5} and seven layers of normal metal YbRhIn_{5}. As n is reduced, the Kondo coherence temperature is suppressed due to the reduction of effective Kondo screening. The Néel temperature is gradually suppressed as n decreases and the quasiparticle mass is strongly enhanced, implying dimensional control toward a quantum critical point. Magnetotransport measurements reveal that a quantum critical point is reached for the n=3 superlattice by applying small magnetic fields. Remarkably, the anisotropy of the quantum critical field is opposite to the expectations from the magnetic susceptibility in bulk CeRhIn_{5}, suggesting that the Rashba spin-orbit interaction arising from the inversion symmetry breaking at the interface plays a key role for tuning the quantum criticality in the two-dimensional Kondo lattice.