This work builds a bridge between density functional theory (DFT) and model interpretations of Anderson's superexchange theory by constructing a $f$-$d$-$p$ model with DFT Wannier functions to enable a direct quantum many-body solution within an embedding approach. When applied to long-range magnetic interactions in a Mn-Ce magnetic molecule, we are able to obtain numerical insights about double exchange and superexchange interactions. Direct metal-metal charge transfer processes are generally weak in this molecule, which leads to small contributions from double exchange interactions. For long-range interactions, Mn-Ce charge transfer is not significant compared to Ce-O charge transfer. The unusual superexchange between Mn atoms with different valence states is identified as the dominant mechanism. This procedure opens a path for quantitative understanding of different exchange interactions in complex magnetic systems, including molecular magnets, transition metal organic frameworks, and other solid materials.