In this research work, we use the generalized Bernoulli equation method (gBEM) to investigate the chaotic nature of solitons in complex structured conformable coupled Maccari system (CCMS) which is a fractional generalization of a nonlinear model coupled Maccari system (CMS) initially created to simulate hydraulic systems. This key model has numerous applications in several disciplines such as hydrodynamics, optics, quantum mechanics and plasma physics. The proposed gBEM converts the CCMS into a set of nonlinear ordinary differential equations (NODEs) to construct fresh plethora of soliton solutions in the form of rational, trigonometric, hyperbolic, and exponential functions. To comprehend the dynamics of acquired solitons in CCMS, a series of 3D and counter plots are used which graphically illustrate and reveal two types of chaotic perturbations, namely axial and periodic perturbations in the acquired solitons. Furthermore, the efficiency and adaptability of our method in handling a range of nonlinear models in mathematical science and engineering are confirmed by our computational work.