Periodic variations in dispersion and nonlinearity are key tools for studying nonlinear wave processes in optics and quantum gases. These variations have led to the dynamical stabilization of BEC (preventing collapse), soliton stabilization in BEC with spin-orbit coupling and stable two-dimensional NLSE solitons and compactons [1]. Most studies focus on dynamical stabilization in scalar two-dimensional cubic NLSE and one-dimensional NLSE with quintic nonlinearities, though collapse phenomena also occur in N-coupled NLSE. For vector two-dimensional NLSE, dynamical stabilization via nonlinearity management has been primarily explored through numerical simulations [2]. This work aims to develop a theoretical analysis of dynamical stabilization of solitons in two-dimensional vector NLSE under strong nonlinearity management.