An evolutionary model for investigating the nonlinear gravito-electrostatic waves in a self-gravitating inhomogeneous planar collisional dust molecular cloud on the Jeans scales of space and time is theoretically proposed. It includes dust-charge variation and weak but finite inertia of the thermal electrons and ions. All the equilibrium gradients and inhomogeneities arising from the dynamics of the electrons, ions, neutral and charged grains are considered simultaneously for the first time. So, any conventional homogenization assumption for mathematical simplification is avoided. By standard inhomogeneous multiple scaling techniques, it is methodologically shown that the fluctuations are collectively governed by a new gravito-electrostatically coupled pair of driven Korteweg–de Vries (d-KdV) equations with new gradient-driven variable coefficients and self-consistent linear sources. A numerical analysis portrays the eigenmode excitations as oscillatory shock- and soliton-like structures. In addition, depending on the explicit regions of the varied plasma parameter space and inhomogeneities, a new shape-transition from soliton to shock and vice versa occurs. Our nonlinear wave analyses could be applied to explain multispace satellite observations and predictions made by others in the past.