Several types of energetic supernovae, such as superluminous supernovae (SLSNe) and broad-line Ic supernovae (Ic-BL SNe), could be powered by the spin-down of a rapidly rotating magnetar. Currently, most models used to infer the parameters for potential magnetar-driven supernovae make several unsuitable assumptions that likely bias the estimated parameters. In this work, we present a new model for magnetar-driven supernovae that relaxes several of these assumptions and an inference workflow that enables accurate estimation of parameters from light curves of magnetar-driven supernovae. In particular, in this model, we include the dynamical evolution of the ejecta, coupling it to the energy injected by the magnetar itself while also allowing for non-dipole spin down. We show that the model can reproduce SLSN and Ic-BL SN light curves consistent with the parameter space from computationally expensive numerical simulations. We also show the results of parameter inference on four well-known example supernovae, demonstrating the model's effectiveness at capturing the considerable diversity in magnetar-driven supernova light curves. The model fits each light curve well and recovers parameters broadly consistent with previous works. This model will allow us to explore the full diversity of magnetar-driven supernovae under one theoretical framework, more accurately characterize these supernovae from only photometric data, and make more accurate predictions of future multiwavelength emission to test the magnetar-driven scenario better.