The properties of functional oxide heterostructures are strongly influenced by the physics governing their interfaces. Modern deposition techniques allow us to accurately engineer interface physics through the growth of atomically precise heterostructures. This enables minute control over the electronic, magnetic, and structural characteristics, which in turn allows for the tuning of the properties of the heterostructures and can even lead to the emergence of properties not present in the individual heterostructure components. Here, we investigate the magnetic properties of tailor-made superlattices employing the ferromagnetic and insulating double perovskites RE₂NiMnO₆ (RE = La, Nd), featuring distinct Curie temperatures. Adjusting the superlattice periodicity at the unit cell level allows us to engineer the magnetic phase diagram. Large periodicity superlattices conserve the individual para- to ferromagnetic transitions of the La₂NiMnO₆ and Nd₂NiMnO₆ parent compounds. As the superlattice periodicity is reduced, the Curie temperatures of the superlattice constituents converge and, finally, collapse into one single transition for the lowest period samples, illustrating that low-periodicity superlattices behave as a unique material. This is a consequence of the magnetic order parameter propagating across the superlattice interfaces, as supported by a minimal Landau theory model. Further, we find that the Nd-Ni-Mn exchange interaction can be enhanced by the superlattice interfaces. This leads to a field-induced reversal of the Nd magnetic moments, as confirmed by synchrotron X-ray magnetic circular dichroism measurements and supported by first-principles calculations. Our work demonstrates how superlattice engineering can be employed to fine-tune the magnetic properties in oxide heterostructures and broadens our understanding of magnetic interfacial effects.