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We present the results of a combined experimental approach on the homoleptic perovskite-like coordination polymer [(CH₃)₂NH₂]Cu(HCOO)₃, where neutron diffraction and magnetisation measurements were used to solve the ground state magnetic structure, while electron charge density distribution and orbital occupancy were determined by high-resolution X-ray diffraction. The latter enabled a microscopic analysis of the chemical bonding in this quasi-1D antifferomagnet, from which we established the mechanism of magnetic exchange through formate anions and criteria for the applicability of Goodenough-Kanamori-Anderson (GKA) rules to superexchange mediated by polyatomic ligands. Moreover, through in-situ, high-pressure x-ray diffraction experiments we showed that [(CH₃)₂NH₂]Cu(HCOO)₃ undergoes a pressure-induced orbital reordering phase transition above 5.20 GPa. This transition is distinct from previously reported Jahn-Teller switching in coordination polymers, which required at least two different ligands that crystallize in a reverse spectrochemical series. We demonstrated that the orbital reordering phase transition in [(CH₃)₂NH₂]Cu(HCOO)₃ is instead primarily driven by unconventional octahedral tilts and shifts of the framework, and/or a reconfiguration of A-site cation ordering. These structural instabilities are unique to the coordination polymer perovskites, and may form the basis for undiscovered orbital reorientation phenomena in this broad family of materials. Moreover, based on the derived criteria for the applicability of GKA rules, we anticipate a change between two different A-type magnetic structures in which the antiferromagnetic stacking direction has switched.