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Using density functional based LDA+U methods and linear–response theory, we study the magnetic exchange interactions of the superconductor Nd_1−xSr_xNiO₂, finding that hole doping significantly enchances the inter-layer exchange coupling compared to the nearest-neighbor interactions. This can be understood as a consequence of the large overlap of the Ni-3d_3z²-r² orbital in the z-direction, in contrast to its small hybridization within the NiO₂ plane which results in a flat band near the Fermi level. Additionally, while previous works emphasize the importance of the Ni-3d_x²-y² and Nd-5d orbitals, we demonstrate that the Nd-5d orbitals have no effect on magnetic exchange interactions, instead proposing a Ni-3d_x²-y²/Ni-3d_3z²-r² two–band model for this material. This model is solved using DMFT, revealing an underlying Mott insulating state, which upon doping produces competing S=0 and S=1 two–hole states at low energies, depending on the precise values of the intra–atomic Hunds coupling.