We perform a detailed analysis of the SO(10) SUSY GUT model with D₃ family symmetry of Dermíšek and Raby (DR). The model is specified in terms of 24 parameters and predicts, as a function of them, the whole MSSM set of parameters at low energy scales. Concerning the SM subset of such parameters, the model is able to give a satisfactory description of the quark and lepton masses, of the PMNS matrix and of the CKM matrix. We perform a global fit to the model, including flavour changing neutral current (FCNC) processes B_s μ⁺μ⁻, B X_sγ, B X_sℓ⁺ℓ⁻ and the B_d,s−B̅_d,s mass differences ΔM_d,s as well as the flavour changing (FC) process B⁺ τ⁺ν. These observables provide at present the most sensitive probe of the SUSY mass spectrum and couplings predicted by the model. Our analysis demonstrates that the simultaneous description of the FC observables in question represents a serious challenge for the DR model, unless the masses of the scalars are moved to regions which are problematic from the point of view of naturalness and probably beyond the reach of the LHC. We emphasize that this problem could be a general feature of SUSY GUT models with third generation Yukawa unification and weak-scale minimal flavour violation.