Droplet-based microfluidics has provided a means to generate multi-core double emulsions, which are versatile platforms for microreactors in materials science, synthetic biology, and chemical engineering. To provide new opportunities for double emulsion platforms, here, we report a glass capillary microfluidic approach to first fabricate osmolarity-responsive Water-in-Oil-in-Water (W/O/W) double emulsion containing two different inner droplets/cores and to then trigger the coalescence between the encapsulated droplets precisely. To achieve this, we independently control the swelling speed and size of each droplet in the dual-core double emulsion by controlling the osmotic pressure between the inner droplets and the collection solutions. When the inner two droplets in one W/O/W double emulsion swell to the same size and reach the instability of the oil film interface between the inner droplets, core-coalescence happens and this coalescence process can be controlled precisely. This microfluidic methodology enables the generation of highly monodisperse dual-core double emulsions and the osmolarity-controlled swelling behavior provides new stimuli to trigger the coalescence between the encapsulated droplets. Such swelling-caused core-coalescence behavior in dual-core double emulsion establishes a novel microreactor for nanoliter-scale reactions, which can protect reaction materials and products from being contaminated or released.