We bring together magnetization, infrared spectroscopy, and lattice dynamics calculations to uncover the magnetic field-temperature ( B- T) phase diagrams and vibrational properties of the [(CH3)2NH2] M(HCOO)3 ( M = Mn2+, Co2+, Ni2+) family of multiferroics. While the magnetically driven transition to the fully saturated state in [(CH3)2NH2]Mn(HCOO)3 takes place at 15.3 T, substitution with Ni or Co drives the critical fields up toward 100 T, an unexpectedly high energy scale for these compounds. Analysis of the infrared spectrum of the Mn and Ni compounds across TC reveals doublet splitting of the formate bending mode which functions as an order parameter of the ferroelectric transition. By contrast, [(CH3)2NH2]Co(HCOO)3 reveals a surprising framework rigidity across the order-disorder transition due to modest distortions around the Co2+ centers. The transition to the ferroelectric state is thus driven by the dimethylammonium cation freezing and the resulting hydrogen bonding. Under applied field, the Mn (and most likely, the Ni) compounds engage the formate bending mode to facilitate the transition to their fully saturated magnetic states, whereas the Co complex adopts a different mechanism involving formate stretching distortions to lower the overall magnetic energy. Similar structure-property relations involving substitution of transition-metal centers and control of the flexible molecular architecture are likely to exist in other molecule-based multiferroics.