Gold-Silver (Au-Ag) core-shell nanostructures are gaining importance in stretchable electronics where high tensile and fatigue resistance is of paramount importance. This work proposes the parameterization of a modified embedded atomic model (MEAM) interatomic potential through density functional theory (DFT) calculations for investigating the role of dislocations and defect interaction governing the mechanical behavior of Au-Ag and Ag-Au Core-shell nanostructures under tensile and fatigue loading using molecular dynamics (MD) simulations. A comparative analysis between the Core-shell structures and their pristine counterparts is also conducted. Throughout this work, pseudo-potential and all-electron full potential DFT schemes are used for parameterizing MEAM by calculating cohesive energy, lattice parameter, and bulk modulus of pure Au, Ag and their alloy. Using the new force-field for MD simulations, the tensile behavior of pristine and core-shell nanowires is explored for temperatures between 300K to 600K. The fatigue properties of two pristine and two core-shell nanowires in a strain range of -15% to 15% for 10 cycles is also conducted. Our results suggest that Ag-Au Core-shell nanowire shows the best reversibility under fatigue loading among the structures examined. Moreover, Ag-Au exhibit the highest dislocation formation and complete annihilation of defects consistently. While, Au-Ag present improved fatigue properties than its pristine counterparts but have some residual defects leading to lower reversibility when compared to Ag-Au. For tensile loading, all four structures exhibited deterioration in strength with increasing temperature. Thermal softening is seen to be more prominent in Au-Ag core-shell nanowires compared to Ag-Au.