The inherent instability of laser welding, particularly keyhole instability, poses significant challenges in industrial applications, leading to defects such as porosities that compromise weld quality. Various forces act on the keyhole and molten pool during laser welding, influencing process stability. These forces are categorized into those promoting keyhole opening and penetration (e.g., recoil pressure) and those promoting keyhole collapse (e.g., surface tension, Darcy's damping forces), increasing instability and defect likelihood. This paper provides a comprehensive instability analysis to uncover key factors affecting keyhole and process instability, presenting future avenues for improving laser welding stability. Using a novel numerical method for simulating laser spot welding on aluminum with COMSOL Multiphysics 5.6, we investigated the effect of laser pulse shaping on keyhole and process instability. Our analysis focused on keyhole morphology, fluid flow behaviour, and force analysis. The results indicated that the curvature effect, Marangoni effect, and Darcy's damping force are primary contributors to instability, with the curvature effect and Darcy's damping force being the most dominant. Additionally, erratic and high-velocity magnitudes induce intense fluid flow behaviour, exacerbating keyhole instability. Moreover, single/quadruple peak triangular and variant rectangular ramp-down pulse shapes produced the least instability, while multi-pulse rectangular shapes exhibited intense instability. It was found that combining triangular/rectangular pulse shapes can reduce force and keyhole instability by smoothing spontaneous force spikes, resulting in a more stabilized welding process. Controlling fluid flow and abrupt force changes with appropriate pulse shaping is key to defect-free welded products.