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 CeRhIn5 and seven layers of normal metal YbRhIn5. 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 CeRhIn5, 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.