An extendable double network design for hydrogels with programmable external geometries and actuating trajectories is presented. Chemically cross-linked polyacrylamide as the first network penetrated with linear alginate chains is prepared for demonstration. The coordination of Fe3+ ions with carboxylate groups in alginate chains acts as the second network, and its dissociation through photoreduction is utilized to realize the photoresponsive shape memory property; the shape fixity ratio and shape recovery ratio both exceed 90%. The gradient dissociation of Fe3+-carboxylate coordination under UV facilitates 3D programming of hydrogel geometry. On another aspect, the resulted cross-linking gradient differentiates the extent and rate of solvent-induced volume change of the PAAm network, endowing the hydrogel with photo-programmable solvent-driven actuating behavior. Furthermore, by inducing the formation of Fe3+-carboxylate coordination within the entire network for shape programming and cross-linking gradients in specific regions as active joints, hydrogels with designed actuating behaviors based on specific 3D shapes are realized. The shape memory and active morphing functionalities enabled by photo-dissociable Fe3+-carboxylate coordination in PAAm hydrogel can be generally extended to other hydrogels.