We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our FASTNC code and integrate it into the CosmoSIS framework. We measure the two-point functions ξ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨Map3⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ωm-S8 plane when we add the ⟨Map3⟩ data to ξ±. We present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.