We undertake a detailed analysis of the non-local properties of the fundamental problem of two trapped, distinguishable neutral atoms that interact with a short-range potential characterized by an s-wave scattering length. We show that this interaction generates continuous variable (CV) entanglement between the external degrees of freedom of the atoms and consider its behaviour as a function of both, the distance between the traps and the magnitude of the inter-particle scattering length. We first quantify the entanglement in the ground state of the system at zero temperature and then, adopting a phase-space approach, test the violation of the Clauser–Horn–Shimony–Holt inequality at zero and non-zero temperature and under the effects of general dissipative local environments.