ABSTRACT The tension between the diverging density profiles in Lambda cold dark matter simulations and the constant-density inner regions of observed galaxies is a long-standing challenge known as the ‘core–cusp’ problem. We demonstrate that the SMUGGLE galaxy formation model implemented in the arepo moving mesh code forms constant-density cores in idealized dwarf galaxies of M⋆ ≈ 8 × 107 Msun with initially cuspy dark matter (DM) haloes of M200 ≈ 1010 Msun. Identical initial conditions run with an effective equation of state interstellar medium model preserve cuspiness. Literature on the subject has pointed to the low density threshold for star formation, ρth, in such effective models as an obstacle to baryon-induced core formation. Using a SMUGGLE run with equal ρth, we demonstrate that core formation can proceed at low density thresholds, indicating that ρth is insufficient on its own to determine whether a galaxy develops a core. We reaffirm that the ability to resolve a multiphase interstellar medium at sufficiently high densities is a more reliable indicator of core formation than any individual model parameter. In SMUGGLE, core formation is accompanied by large degrees of non-circular motion, with gas rotational velocity profiles that consistently fall below the circular velocity $v_\text{circ} = \sqrt{GM/R}$ out to ∼2 kpc. Asymmetric drift corrections help recover the average underlying DM potential for some of our less efficient feedback runs, but time-variations in the instantaneous azimuthal gas velocity component are substantial, highlighting the need for careful modelling in the inner regions of dwarfs to infer the true distribution of DM.