The present work considers dual-solution behaviour of radiative hybrid nanofluid flow of sodium alginate containing aluminium alloys (AA7072 and AA7075) past a power-law stretching/shrinking sheet with suction. This understanding of such flow is important because of applications in thermal energy systems, biomedical devices, and aerospace cooling technology. The governing nonlinear boundary layer equations have been transformed using similarity variables and then solved numerically using the MATLAB bvp4c solver. The influence of the magnetic field, thermal radiation, suction, volume fractions of the nanoparticles, thermal slip, and chemical reactions on the velocity, temperature, and concentration profiles has been discussed in the analysis. It is found that the temperature profile increased by 15.6% due to the increase of the radiation parameter and heat source term. In comparison, the velocity approached the wall decreased by 12.3% due to the increase of the modifier parameter. The suction leads to better stability for the boundary layer, while increasing the values of the Prandtl and Schmidt numbers enhances the thermal and concentration boundary layer thickness. In certain ranges of both the suction rate and the stretching/shrinking rates, there exist dual solutions that indicate a bifurcation of the flow and a sensitivity of the stability. The new addition to existing models presented in this work is the mixture of sodium alginate with dual aluminium alloy nanoparticles under the influence of both radiative and MHD effects, allowing for new perspectives in hybrid nanofluid control mechanisms. These findings can be applied to increase the efficiency of heat and mass transfer in new, high-tech industrial and biomedical systems.