A dual-porosity model is proposed to describe low and high valence ion transport in swelling clays characterized by three separate-length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the finest (nano) scale the medium is composed of charged clay particles saturated by aqueous electrolyte solution containing monovalent and divalent ions. Assuming local equilibrium with the bulk fluid lying in the micropores, the disjoining pressure is computed exploring the tools of Statistical Mechanics based on an integral equation theory which, in contrast to monovalent ions, predicts attractive forces between particles for multivalent ions due to incorporation of the ion-ion correlation effects. At the intermediate microscale, the two-phase homogenized system is represented by swollen clay clusters (or aggregates) with the nanoscale disjoining pressure incorporated in a modified form of Terzaghi's effective principle. At the macroscale, the system of clay clusters is homogenized with the bulk fluid. The resultant macroscopic picture is governed by a dual-porosity model wherein ion transport takes place in the bulk solution and the clay clusters act as sources/sinks to the bulk fluid. The quasi-steady version of the dual-porosity model allows to build-up numerically the constitutive behavior of the retardation coefficient governing adsorption within the clay clusters. The three-scale model is applied to numerically simulate the migration of monovalent and divalent ions in a compacted clay liner underneath a sanitary landfill. Owing to the distinct constitutive behavior of the swelling pressure for each ionic species, totally different evolving regimes are observed for calcium and sodium diffusion through the clay liner.