We investigate the existence and uniqueness of solutions to the second kind of generalized nonlinear Volterra-Fredholm integral equations (GNV-FIEs). These equations are analyzed using the Banach fixed point theorem and Picard’s approach, particularly in situations where Picard’s method might not work. We also present a new numerical method which incorporates quadrature principles, including Simpson’s 3/8 and Romberg, with the modified Adomian decomposition method (MADM). This method can be extremely effective when calculating definite integrals becomes challenging. We begin our paper with a brief overview of the topic and then go into great detail into the suggested approach. We then illustrate the applicability of the theoretical results through numerical examples, which are presented in tables and figures for clarity.