The capillary effect caused by the interfacial energy dominates the dynamics of small droplets, particularly the contact lines (where three phases meet). With insoluble surfactant laid on the capillary surface, the adhesion of droplets to some textured substrates becomes more complicated: (i) insoluble surfactant disperses along the evolving capillary surface (ii) the surfactant-dependent surface tension will in turn drive the full dynamics of droplets, particularly the moving contact lines. Using Onsager’s principle with different Rayleigh dissipation functionals, we derive and compare both the geometric motion of the droplets and the viscous flow model with Marangoni effect. To enforce impermeable obstacle constraint, the full dynamics of the droplet can be formulated as a gradient flow on a manifold with boundary, and two equivalent variational inequalities are derived. We propose unconditionally stable first/second order numerical schemes based on explicit moving boundaries and arbitrary-Lagrangian Eulerian method. After adapting a projection method for the variational inequality with phase transition information at emerged contact lines, we compute the contact angle hysteresis, unavoidable splitting/merging of droplets on inclined textured substrates