Double-network (DN) hydrogels are promising materials for tissue engineering due to their biocompatibility, high strength, and toughness, but understanding of their microstructure–property relationships still remains limited. This work investigates a DN hydrogel comprising a physically crosslinked agarose, as the first network, and a chemically crosslinked copolymer with a varying ratio of acrylamide and acrylic acid, as the second network. The charge, intrinsic to most DN hydrogels, introduces a responsive behavior to chemical and electrical stimuli. The DN strengthens agarose hydrogels, but the strengthening decreases with the swelling ratio resulting from increasing acrylic acid content or reducing salt concentration. Through careful imaging by atomic force microscopy, the heterogenous surface structure and properties arising from the DN are resolved, while the lubrication mechanisms are elucidated by studying the heterogeneous frictional response to extrinsic stimuli. This method reveals the action of the first (agarose) network (forming grain boundaries), copolymer-rich and poor regions (in grains), charge and swelling in providing lubrication. Friction arises from the shear of the polymeric network, whereas hydrodynamic lift and viscoelastic deformation become more significant at higher sliding velocities. We identify the copolymer-rich phase as the main source of the stimulus-responsive behavior. Salt concentration enhances effective charge density and reduces viscoelastic deformation, while electric bias swells the gel and improves lubrication. This work also demonstrates the dynamic control of interfacial properties like hydrogel friction and adhesion, which has implications for other areas of study like soft robotics and tissue replacements.