We present multitracer dynamical models of the low-mass (M* ∼ 107), isolated dwarf irregular galaxy WLM in order to simultaneously constrain the inner slope of the dark matter (DM) halo density profile (γ) and flattening (qDM), and the stellar orbital anisotropy (βz, βr). For the first time, we show how jointly constraining the mass distribution from the H I gas rotation curve and solving the Jeans equations with discrete stellar kinematics lead to a factor of ∼2 reduction in the uncertainties on γ. The mass-anisotropy degeneracy is also partially broken, leading to reductions on uncertainty by ${\sim} 30{{\ \rm per\ cent}}$ on Mvir (and ${\sim} 70{{\ \rm per\ cent}}$ at the half-light radius) and ${\sim} 25{{\ \rm per\ cent}}$ on anisotropy. Our inferred value of γ = 0.3 ± 0.1 is robust to the halo geometry, and in excellent agreement with predictions of stellar feedback-driven DM core creation. The derived prolate geometry of the DM halo with qDM = 2 ± 1 is consistent with Lambda cold dark matter simulations of dwarf galaxy haloes. While self-interacting DM (SIDM) models with σ/mX ∼ 0.6 can reproduce this cored DM profile, the interaction events may sphericalize the halo. The simultaneously cored and prolate DM halo may therefore present a challenge for SIDM. Finally, we find that the radial profile of stellar anisotropy in WLM (βr) follows a nearly identical trend of increasing tangential anisotropy to the classical dwarf spheroidals, Fornax and Sculptor. Given WLM's orbital history, this result may call into question whether such anisotropy is a consequence of tidal stripping in only one pericentric passage or if it instead is a feature of the largely self-similar formation and evolutionary pathways for some dwarf galaxies.